<PAGE>   1

                                                                     EXHIBIT 2.3

                                 AMENDMENT NO. 1
                                       to
                          AGREEMENT AND PLAN OF MERGER
                                     between
                         THERMADYNE HOLDINGS CORPORATION
                                       and
                         MERCURY ACQUISITION CORPORATION

         AMENDMENT NO. 1 TO AGREEMENT AND PLAN OF MERGER (this "AMENDMENT"),
dated as of April 22, 1998, by and between Thermadyne Holdings Corporation, a
Delaware corporation (the "COMPANY"), and Mercury Acquisition Corporation, a
Delaware corporation ("MERGERSUB").

                                   WITNESSETH:
         WHEREAS, MergerSub and the Company are parties to an Agreement and Plan
of Merger dated as of January 20, 1998 (the "AGREEMENT"); and

         WHEREAS, the parties desire to amend the Agreement in certain respects;

         NOW, THEREFORE, in consideration of the premises and mutual agreements
set forth herein and in the Agreement, the parties hereto agree as follows:

         1. Section 1.07(a) is hereby amended by deleting the opening clause
"Except as set forth on Schedule 1.07(a)," so that Section 1.07(a) now commences
with the word "Immediately."

         2. Schedule 1.07(a) is hereby deleted in its entirety.

         3. Section 1.07(b) is renumbered 1.07(c) and the reference therein to
Section 1.07(a) is hereby amended to refer to Sections 1.07(a) and 1.07(b), and
a new Section 1.07(b) is hereby inserted as follows:

                  (b) At the Effective Time, each outstanding right to purchase
                  Shares with previously held funds under the Employee Stock
                  Purchase Plan (the "ESPP") shall be canceled. In lieu thereof,
                  as soon as reasonably practicable as of or after the Effective
                  Time, the holders of such purchase rights shall receive a cash
                  payment from the Company equal to the product of (i) the total
                  number of Shares of Company Common Stock subject to such
                  purchase rights immediately prior to the Effective Time and
                  (ii) $34.50. All funds previously withheld under the ESPP will
                  become assets of the Company.

         4. Section 5.08 is hereby amended to read as follows:


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                                                                          Page 2

                  "[intentionally omitted]."

         5. Section 8.02(f) of the Agreement is hereby deleted in its entirety,
and Section 8.02(g) is renumbered 8.02(f).

         6. Exhibit A of the Agreement is hereby amended to read in its entirety
as follows:



                   "SECOND AMENDED AND RESTATED CERTIFICATE OF
                                 INCORPORATION



                                     OF THE



                              SURVIVING CORPORATION



                                      *****



         As of the Effective Time, the Certificate of Incorporation of the
Surviving Corporation, as amended and restated hereby, shall, upon its filing
with the Secretary of State of the State of Delaware, read in its entirety as
follows:

         FIRST:  The name of the Corporation is Thermadyne Holdings Corporation.

         SECOND: The address of its registered office in the State of Delaware
is 1013 Centre Road, Wilmington, Delaware 19805. The name of its registered
agent at such address is Corporation Service Company.

         THIRD: The purpose of the Corporation and the nature and objects of the
business to be transacted, promoted, and carried on are to engage in any lawful
act or activity for which corporations may be organized under the General
Corporation Law of the State of Delaware, as the same exists or may hereafter be
amended (the "Delaware Law").




<PAGE>   3
                                                                          Page 3

         FOURTH: The total number of shares of stock which the Corporation shall
have authority to issue is 45,000,000, consisting of 30,000,000 shares of Common
Stock, par value $0.01 per share (the "COMMON STOCK"), and 15,000,000 shares of
Preferred Stock, par value $0.01 per share (the "PREFERRED STOCK"), of which
2,000,000 shares have been designated 13% Senior Exchangeable Preferred Stock
(the "SENIOR PREFERRED STOCK").

         The designations and the powers and preferences, rights,
qualifications, limitations and restrictions of the Common Stock and the
Preferred Stock are as follows:

         A.       Provisions Relating to the Common Stock

         Except as otherwise required by law, each holder of Common Stock shall
be entitled to one vote for each share of common stock standing in such holder's
name on the records of the Corporation on each matter submitted to a vote of the
stockholders.

         The holders of the Common Stock shall be entitled to receive when, as,
and if declared by the board of directors of the Corporation, out of funds
legally available therefor, dividends payable in cash, stock, or otherwise.

         Upon any liquidation, dissolution, or winding up of the Corporation,
whether voluntary or involuntary, and after the holders of any bonds,
debentures, or other obligations of the Corporation shall have been paid in full
the amounts to which they shall be entitled (if any), or a sum sufficient for
such payment in full shall have been set aside, the remaining net assets of the
Corporation shall be distributed pro rata to the holders of the Common Stock in
accordance with their respective rights and interests, to the exclusion of the
holders of any bonds, debentures, or other obligations of the Corporation.

         The Corporation may issue shares of its Common Stock from time to time
for such consideration (in any form, but not less in value than the par value
thereof) as may be fixed by the board of directors of the Corporation, which is
expressly authorized to fix the same in its absolute and uncontrolled discretion
subject to the foregoing conditions. Shares so issued for which the
consideration shall have been paid or delivered to the Corporation shall be
deemed fully paid stock and shall not be liable to any further call or
assessment thereon, and the holders of such shares shall not be liable for any
further payments in respect of such shares. The Corporation shall also have
authority to create and issue rights and options entitling their holders
to purchase or otherwise acquire shares of Common Stock and such rights and
options shall be evidenced by instrument(s) approved by the board of directors
of the Corporation. The board of directors of the Corporation shall be empowered
to set the exercise price, duration, times for exercise, and other terms of such
options or rights; provided, however, that the consideration to be received
(which may be in any form) for any shares of Common Stock subject thereto shall
have a value not less than the par value thereof.

<PAGE>   4
                                                                          Page 4

         B.       Provisions Relating to the Preferred Stock

         The Board of Directors is hereby empowered to authorize by resolution
or resolutions from time to time the issuance of one or more classes or series
of Preferred Stock and to fix the designations, powers, preferences and
relative, participating, optional or other rights, if any, and the
qualifications, limitations or restrictions thereof, if any, with respect to
each such class or series of Preferred Stock and the number of shares
constituting each such class or series, and to increase or decrease the number
of shares of any such class or series to the extent permitted by the Delaware
Law.

         C.       Provisions Relating to the Senior Preferred Stock

         (1) NUMBER AND DESIGNATION. 2,000,000 shares of the Preferred Stock of
the Corporation shall be designated as 13% Senior Exchangeable Preferred Stock.

         (2) RANK. The Senior Preferred Stock shall, with respect to dividend
rights and rights on liquidation, dissolution and winding up, rank prior to all
classes of or series of common stock of the Corporation, including the
Corporation's Common Stock, and each other class of capital stock of the
Corporation, the terms of which provide that such class shall rank junior to the
Senior Preferred Stock or the terms of which do not specify any rank relative to
the Senior Preferred Stock. All equity securities of the Corporation to which
the Senior Preferred Stock ranks prior (whether with respect to dividends or
upon liquidation, dissolution, winding up or otherwise), including the Common
Stock, are collectively referred to herein as the "JUNIOR SECURITIES." All
equity securities of the Corporation with which the Senior Preferred Stock ranks
on a parity (whether with respect to dividends or upon liquida tion, dissolution
or winding up) are collectively referred to herein as the "PARITY SECURITIES."
The respective definitions of Junior Securities and Parity Securities shall also
include any rights or options exercisable for or convertible into any of the
Junior Securities and Parity Securities, as the case may be. The Senior
Preferred Stock shall be subject to the creation of Junior Securities.

                  (3) DIVIDENDS. (a) (i) The holders of shares of Senior
Preferred Stock shall be entitled to receive, when, as and if declared by the
Board of Directors, out of funds legally available for the payment of dividends,
dividends (subject to Sections 3(a)(ii) and (iii) hereof) at a rate equal to
______ [the greater of (x) 13% per annum (computed on the basis of a 360 day
year) or (y) the stated rate of interest per annum payable on the Senior
Subordinated Notes due 2008 of Thermadyne Mfg. LLC plus 300 basis points] (the
"DIVIDEND RATE") on the Liquidation Value of each share of Senior Preferred
Stock on and as of the most recent Dividend Payment Date (as defined below). In
the event the Corporation is unable or shall fail to discharge its obligation to
redeem all 

<PAGE>   5

                                                                          Page 5

outstanding shares of Senior Preferred Stock pursuant to paragraph 5(c) or 5(d)
hereof, the Dividend Rate shall increase by .25 percent per quarter (each, a
"DEFAULT DIVIDEND") for each quarter or portion thereof following the date on
which such redemption was required to be made until cured, provided that the
aggregate increase shall not exceed 5%. Such dividends shall be payable in the
manner set forth below in Sections 3(a)(ii) and (iii) quarterly on March 31,
June 30, September 30, and December 31 of each year (unless such day is not a
business day, in which event on the next succeeding business day) (each of such
dates being a "DIVIDEND PAYMENT DATE" and each such quarterly period being a
"DIVIDEND PERIOD"). Such dividends shall be cumulative from the date of issue,
whether or not in any Dividend Period or Periods there shall be funds of the
Corporation legally available for the payment of such dividends.

                  (ii) Prior to the fifth anniversary of the issuance of the
                  Senior Preferred Stock (the "CASH PAY DATE"), dividends shall
                  not be payable in cash to holders of shares of Senior
                  Preferred Stock but shall, subject to Section 3(b) hereof,
                  accrete to the Liquidation Value in accordance with Section
                  4(a) hereof.

                   (iii) Following the Cash Pay Date, each such dividend shall
                  be payable in cash on the Liquidation Value per share of the
                  Senior Preferred Stock, in equal quarterly amounts (to which
                  the Default Dividend, if any, shall be added), to the holders
                  of record of shares of the Senior Preferred Stock, as they
                  appear on the stock records of the Corporation at the close of
                  business on such record dates, not more than 60 days or less
                  than 10 days preceding the payment dates thereof, as shall be
                  fixed by the Board of Directors. Accrued and unpaid dividends
                  for any past Dividend Periods may be declared and paid at any
                  time, without reference to any Dividend Payment Date, to
                  holders of record on such date, not more than 45 days
                  preceding the payment date thereof, as may be fixed by the
                  Board of Directors.

         (b) At the written request of the holders of a majority of the shares
of Senior Preferred Stock, the Corporation shall, commencing on the first
Dividend Payment Date after such request and ending on the Cash Pay Date, be
required to pay all dividends on shares of Senior Preferred Stock by the
issuance of additional shares of Senior Preferred Stock ("ADDITIONAL SHARES").
The Additional Shares shall be identical to all other shares of Senior Preferred
Stock, except as set forth in Section 4. For the purposes of determining the
number of Additional Shares to be issued as dividends pursuant to this Paragraph
(b), such Additional Shares shall be valued at their Applicable Liquidation
Value as provided in Section 4(c).

         (c) Holders of shares of Senior Preferred Stock shall not be entitled
to any dividends, whether payable in cash, property or stock, in excess of the
cumulative dividends, as herein provided, on the Senior Preferred Stock. Except

<PAGE>   6
                                                                          Page 6


as provided in this Section 3, no interest, or sum of money in lieu of interest,
shall be payable in respect of any dividend payment or payments on the Senior
Preferred Stock that may be in arrears.

         (d) So long as any shares of the Senior Preferred Stock are
outstanding, no dividends, except as described in the next succeeding sentence,
shall be declared or paid or set apart for payment on Parity Securities, for any
period unless (to the extent such dividends are payable in cash) full cumulative
dividends have been or contemporaneously are declared and paid or declared and a
sum sufficient for the payment thereof set apart for such payment on the Senior
Preferred Stock for all Dividend Periods terminating on or prior to the date of
payment of the dividend on such class or series of Parity Securities. When (to
the extent such dividends are payable in cash) dividends are not paid in full or
a sum sufficient for such payment is not set apart, as aforesaid, all dividends
declared upon shares of the Senior Preferred Stock and all dividends declared
upon any other class or series of Parity Securities shall (in each case, to the
extent payable in cash) be declared ratably in proportion to the respective
amounts of dividends accumulated and unpaid on the Senior Preferred Stock and
accumulated and unpaid on such Parity Securities.

         (e) So long as any shares of the Senior Preferred Stock are
outstanding, no dividends (other than dividends or distributions paid in shares
of, or options, warrants or rights to subscribe for or purchase shares of,
Junior Securities) shall be declared or paid or set apart for payment or other
distribution declared or made upon Junior Securities, nor shall any Junior
Securities be redeemed, purchased or otherwise acquired (other than a
redemption, purchase or other acquisition of shares of Common Stock made for
purposes of an employee incentive or benefit plan of the Corporation or any
subsidiary) (all such dividends, distributions, redemptions or purchases being
hereinafter referred to as a "JUNIOR SECURITIES DISTRIBUTION") for any
consideration (or any moneys be paid to or made available for a sinking fund for
the redemption of any shares of any such stock) by the Corporation, directly or
indirectly (except by conversion into or exchange for Junior Securities), unless
in each case (i) the full cumulative dividends on all outstanding shares of the
Senior Preferred Stock and any other Parity Securities shall (to the extent
payable in cash) have been paid or set apart for payment for all past Dividend
Periods with respect to the Senior Preferred Stock and all past dividend periods
with respect to such Parity Securities and (ii) (to the extent payable in cash)
sufficient funds shall have been paid or set apart for the payment of the
dividend for the current Dividend Period with respect to the Senior Preferred
Stock and the current dividend period with respect to such Parity Securities.

         (4) LIQUIDATION PREFERENCE. (a) In the event of any liquidation,
dissolution or winding up of the Corporation, whether voluntary or involuntary,
before any payment or distribution of the assets of the Corporation (whether
capital or surplus) shall be made to or set apart for the holders of Junior
Securities, the holders of the shares of Senior Preferred Stock shall be
entitled to 

<PAGE>   7
                                                                          Page 7

receive an amount equal to the Liquidation Value of such share plus
any accrued and unpaid cash dividends to the date of distribution. "LIQUIDATION
VALUE" on any date means, with respect to (x) any share of Senior Preferred
Stock other than any Additional Shares, the sum of (1) $25.00 per share and (2)
the aggregate of all dividends accreted on such share until the most recent
Dividend Payment Date upon which an accretion to Liquidation Value has occurred
(or if such date is a Dividend Payment Date upon which an accretion to
Liquidation Value has occurred, such date), provided that in the event of an
actual liquidation, dissolution or winding up of the Corporation or the
redemption of any shares of Senior Preferred Stock pursuant to Section 5
hereunder, the amount referred to in (2) shall be calculated by including
dividends accreting to the actual date of such liquidation, dissolution or
winding up or the redemption date, as the case may be, rather than the Dividend
Payment Date referred to above and provided further that in no event will
dividends accrete beyond the earlier of (i) the Cash Pay Date and (ii) the most
recent Dividend Payment Date prior to the Dividend Payment Date on which
dividends on the Senior Preferred Stock are payable in Additional Shares and (y)
any Additional Share, the Applicable Liquidation Value. All accretions to
Liquidation Value will be calculated using compounding on a quarterly basis.
Except as provided in the preceding sentences, holders of shares of Senior
Preferred Stock shall not be entitled to any distribution in the event of
liquidation, dissolution or winding up of the affairs of the Corporation. If,
upon any liquidation, dissolution or winding up of the Corporation, the assets
of the Corporation, or proceeds thereof, distributable among the holders of the
shares of Senior Preferred Stock shall be insufficient to pay in full the
preferential amount aforesaid and liquidating payments on any Parity Securities,
then such assets, or the proceeds thereof, shall be distributed among the
holders of shares of Senior Preferred Stock and any such other Parity Securities
ratably in accordance with the respective amounts that would be payable on such
shares of Senior Preferred Stock and any such other stock if all amounts payable
thereon were paid in full. For the purposes of this Section 4, (i) a
consolidation or merger of the Corporation with one or more corporations, or
(ii) a sale or transfer of all or substantially all of the Corporation's assets,
shall not be deemed to be a liquidation, dissolution or winding up, voluntary or
involuntary, of the Corporation.

         (b) Subject to the rights of the holders of any Parity Securities,
after payment shall have been made in full to the holders of the Senior
Preferred Stock, as provided in this paragraph (4), any other series or class or
classes of Junior Securities shall, subject to the respective terms and
provisions (if any) applying thereto, be entitled to receive any and all assets
remaining to be paid or distributed, and the holders of the Senior Preferred
Stock shall not be entitled to share therein.

         (c) The Applicable Liquidation Value of any Additional Shares shall be
the Liquidation Value of Senior Preferred Stock outstanding immediately prior to
the first Dividend Payment Date occurring after a request for payment in
Additional Shares has been made in accordance with Section 3(b).

<PAGE>   8
                                                                          Page 8


         (5) REDEMPTION. (a) Redemption Upon Consummation of Public Offering.
The Corporation may, at its option, to the extent it shall have funds legally
available for such payment, redeem, prior to May 15, 2001, in whole but not in
part, shares of Senior Preferred Stock, at a redemption price per share equal to
113% of the Liquidation Value, in cash, plus accrued and unpaid cash dividends
on such shares to the date fixed for redemption, without interest, provided that
the Corporation shall not redeem any shares of Senior Preferred Stock pursuant
to this Section 5(a) unless (i) prior to such redemption a Public Offering shall
have been consummated, and (ii) the aggregate redemption price of the shares of
Senior Preferred Stock redeemed pursuant to this Section 5(a) does not exceed
the net proceeds received by the Corporation in such Initial Public Offering.

         "PUBLIC OFFERING" shall mean any underwritten public offering of Common
Stock pursuant to an effective registration statement under the Securities Act
of 1933, as amended, and shall, in addition, for the purposes of Section 5(a)
hereof, include any sale, pursuant to such an underwritten registered public
offering, following the Closing Date of any common stock by any affiliate of the
Corporation, the net proceeds of which are contributed or loaned to the
Corporation in such a manner that such proceeds may lawfully be used for the
redemption of the Senior Preferred Stock.

         "CLOSING DATE" shall have the meaning ascribed to such term in the
Investors' Agreement.

         "INVESTORS' AGREEMENT" means the Investors' Agreement dated May __,
1998, among Thermadyne Holdings Corporation, DLJ Merchant Banking Partners II,
L.P., DLJ Merchant Banking Partners II-A, L.P., DLJ Offshore Partners, C.V., DLJ
Merchant Banking Funding, Inc., DLJ Offshore Partners II, C.V., DLJ Diversified
Partners, L.P., DLJ Diversified Partners-A, L.P., DLJ Millennium Partners, L.P.,
DLJ Millennium-A, L.P., DLJMB Funding II, Inc., DLJ EAB Partners, L.P., DLJ
First ESC L.P., UK Investment Plan 1997 Partners, DLJ ESC II, L.P.
(collectively, the "DLJMB Funds"), and certain other stockholders listed on the
signature pages thereof.

         (b) Redemption At the Option of the Corporation. On and after May 15,
2003, to the extent the Corporation shall have funds legally available for such
payment, the Corporation may, at its option, redeem shares of Senior Preferred
Stock, at any time in whole but not in part, at redemption prices per share in
cash set forth in the table below, together with accrued and unpaid cash
dividends thereon to the date fixed for redemption, without interest:

<PAGE>   9
                                                                          Page 9

<TABLE>
<CAPTION>

           Twelve Months Beginning
                    May 15,                                   Percentage of Liquidation Value
                    ------                                    -------------------------------
                   <S>                                               <C>     
                     2003                                              106.500%
                     2004                                              104.333
                     2005                                              102.167
                     2006                                              100.000
</TABLE>


                  (c) Redemption In the Event of a Change of Control. In the
event of a Change of Control, the Corporation shall, to the extent it shall have
funds legally available for such payment, offer to redeem all of the shares of
Senior Preferred Stock then outstanding, and shall redeem the shares of Senior
Preferred Stock of any holder of such shares that shall consent to such
redemption, upon a date no later than 30 days following the Change in Control,
at a redemption price per share equal to 101% of the Liquidation Value, in cash,
plus accrued and unpaid cash dividends thereon to the date fixed for redemption,
without interest.

         "CHANGE OF CONTROL" means such time as: (a) a "person" or "group"
(within the meaning of Sections 13(d) and 14(d)(2) of the Securities Exchange
Act of 1934, as amended), other than any person or group comprised solely of the
Initial Investors, has become the beneficial owner, by way of merger,
consolidation or otherwise, of 30% or more of the voting power of all classes of
voting securities of the Corporation, and such person or group has become the
beneficial owner of a greater percentage of the voting power of all classes of
voting securities of the Corporation than that beneficially owned by the Initial
Investors; or (b) a sale or transfer of all or substantially all of the assets
of the Corporation to any person or group (other than any group consisting
solely of the Initial Investors or their affiliates) has been consummated; or
(c) during any period of two consecutive years, individuals who at the beginning
of such period constituted the Board of Directors of the Corporation (together
with any new directors whose election was approved by a vote of a majority of
the directors then still in office, who either were directors at the beginning
of such period or whose election or nomination for the election was previously
so approved) cease for any reason to constitute a majority of the directors of
the Corporation, then in office.

         "INITIAL INVESTORS" means the Stockholders (determined as of the
issuance of the Preferred Stock) and their Permitted Transferees, each as
defined in the Investors' Agreement.

         (d) Mandatory Redemption. To the extent the Corporation shall have
funds legally available for such payment, on May 15, 2010, if any shares of the
Senior Preferred Stock shall be outstanding, the Corporation shall redeem all

<PAGE>   10
                                                                         Page 10

outstanding shares of the Senior Preferred Stock, at a redemption price equal to
the aggregate Liquidation Value, in cash, together with any accrued and unpaid
cash dividends thereon to the date fixed for redemption, without interest.

         (e) Status of Redeemed Shares. Shares of Senior Preferred Stock which
have been issued and reacquired in any manner, including shares purchased or
redeemed, shall (upon compliance with any applicable provisions of the laws of
the State of Delaware) have the status of authorized and unissued shares of the
class of Preferred Stock undesignated as to series and may be redesignated and
reissued as part of any series of the Preferred Stock; provided that no such
issued and reacquired shares of Senior Preferred Stock shall be reissued or sold
as Senior Preferred Stock.

         (f) Failure to Redeem. If the Corporation is unable or shall fail to
discharge its obligation to redeem all outstanding shares of Senior Preferred
Stock pursuant to paragraph (5)(c) or 5(d) (each, a "MANDATORY REDEMPTION
OBLIGATION"), such Mandatory Redemption Obligation shall be discharged as soon
as the Corporation is able to discharge such Mandatory Redemption Obligation. If
and so long as any Mandatory Redemption Obligation with respect to the Senior
Preferred Stock shall not be fully discharged, the Corporation shall not (i)
directly or indirectly, redeem, purchase, or otherwise acquire any Parity
Security or discharge any mandatory or optional redemption, sinking fund or
other similar obligation in respect of any Parity Securities (except in
connection with a redemption, sinking fund or other similar obligation to be
satisfied pro rata with the Senior Preferred Stock) or (ii) in accordance with
paragraph 3(e), declare or make any Junior Securities Distribution, or, directly
or indirectly, discharge any mandatory or optional redemption, sinking fund or
other similar obligation in respect of the Junior Securities.

         (g) Failure to Pay Dividends. Notwithstanding the foregoing provisions
of this paragraph (5), unless full cumulative cash dividends (whether or not
declared) on all outstanding shares of Senior Preferred Stock shall have been
paid or contemporaneously are declared and paid or set apart for payment for all
dividend periods terminating on or prior to the applicable redemption date, none
of the shares of Senior Preferred Stock shall be redeemed, and no sum shall be
set aside for such redemption, unless shares of Senior Preferred Stock are
redeemed pro rata.

         (6) PROCEDURE FOR REDEMPTION. (a) In the event the Corporation shall
redeem shares of Senior Preferred Stock pursuant to Sections 5(a), (b) or (d),
notice of such redemption shall be given by first class mail, postage prepaid,
mailed not less than 30 days nor more than 60 days prior to the redemption date,
to each holder of record of the shares to be redeemed at such holder's address
as the same appears on the stock register of the Corporation; provided that
neither the failure to give such notice nor any defect therein shall affect the
validity of the giving of notice for the redemption of any share of Senior
Preferred Stock to be redeemed except as to the holder to whom the Corporation
has 

<PAGE>   11
                                                                         Page 11

failed to give said notice or except as to the holder whose notice was
defective. Each such notice shall state: (i) the redemption date; (ii) the
number of shares of Senior Preferred Stock to be redeemed; (iii) the redemption
price; (iv) the place or places where certificates for such shares are to be
surrendered for payment of the redemption price; and (v) that dividends on the
shares to be redeemed will cease to accrue on such redemption date.

         (b) In the case of any redemption pursuant to Sections 5(a), (b) or (d)
hereof, notice having been mailed as provided in Section 6(a) hereof, from and
after the redemption date (unless default shall be made by the Corporation in
providing money for the payment of the redemption price of the shares called for
redemption), dividends on the shares of Senior Preferred Stock so called for
redemption shall cease to accrue, and all rights of the holders thereof as
stockholders of the Corporation (except the right to receive from the
Corporation the redemption price) shall cease. Upon surrender in accordance with
said notice of the certificates for any shares so redeemed (properly endorsed or
assigned for transfer, if the Board of Directors of the Corporation shall so
require and the notice shall so state), such share shall be redeemed by the
Corporation at the redemption price aforesaid. In case fewer than all the shares
represented by any such certificate are redeemed, a new certificate shall be
issued representing the unredeemed shares without cost to the holder thereof.

         (c) In the case of a redemption pursuant to Section 5(c) hereof, notice
of such redemption shall be given by first class mail, postage prepaid, mailed
not more than 10 days following the occurrence of the Change of Control and not
less than 20 days prior to the redemption date, to each holder of record of the
shares to be redeemed at such holder's address as the same appears on the stock
register of the Corporation; provided that neither the failure to give such
notice nor any defect therein shall affect the validity of the giving of notice
for the redemption of any share of Senior Preferred Stock to be redeemed except
as to the holder to whom the Corporation has failed to give said notice or
except as to the holder whose notice was defective. Each such notice shall
state: (i) that a Change of Control has occurred; (ii) the redemption date;
(iii) the redemption price; (iv) that such holder may elect to cause the
Corporation to redeem all or any of the shares of Senior Preferred Stock held by
such holder; (v) the place or places where certificates for such shares are to
be surrendered for payment of the redemption price; and (vi) that dividends on
the shares the holder elects to cause the Corporation to redeem will cease to
accrue on such redemption date.

         Upon receipt of such notice, the holder shall, within 20 days of
receipt thereof, return such notice to the Corporation indicating the number of
shares of Senior Preferred Stock such holder shall elect to cause the
Corporation to redeem, if any.

         (d) In the case of a redemption pursuant to Section 5(c) hereof, notice
having been mailed as provided in Section 6(c) hereof, from and after the
redemption date (unless default shall be made by the Corporation in providing

<PAGE>   12
                                                                         Page 12

money for the payment of the redemption price of the shares called for
redemption), dividends on such shares of Senior Preferred Stock as the holder
elects to cause the Corporation to redeem shall cease to accrue, and all rights
of the holders thereof as stockholders of the Corporation (except the right to
receive from the Corporation the redemption price) shall cease. Upon surrender
in accordance with said notice of the certificates for any shares so redeemed
(properly endorsed or assigned for transfer, if the Board of Directors of the
Corporation shall so require and the notice shall so state), such share shall be
redeemed by the Corporation at the redemption price aforesaid. In case fewer
than all the shares represented by any such certificate are redeemed, a new
certificate shall be issued representing the unredeemed shares without cost to
the holder thereof.

         (7) EXCHANGE. (a) Subject to the provisions of this paragraph (7) the
Corporation may, at its option, at any time and from time to time on any
Dividend Payment Date, exchange, to the extent it is legally permitted to do so,
all, but not less than all, outstanding shares (and fractional shares) of Senior
Preferred Stock, for Exchange Debentures, provided that (i) on or prior to the
date of exchange the Corporation shall have paid to or declared and set aside
for payment to the holders of outstanding shares of Senior Preferred Stock all
accrued and unpaid cash dividends on shares of Senior Preferred Stock through
the exchange date in accordance with the next succeeding paragraph; (ii) no
event of default under the indenture (as defined in such indenture) governing
the Exchange Debentures shall have occurred and be continuing; and (iii) no
shares of Senior Preferred Stock are held on such date by the DLJMB Funds or any
of their Affiliates, or any of their Permitted Transferees. The principal amount
of Exchange Debentures deliverable upon exchange of a share of Senior Preferred
Stock, adjusted as hereinafter provided, shall be determined in accordance with
the Exchange Ratio (as defined below).

         Cash dividends on any shares of Senior Preferred Stock exchanged for
Exchange Debentures which have accrued but have not been paid as of the date of
exchange shall be paid in cash. In no event shall the Corporation issue Exchange
Debentures in denominations other than $1,000 or in an integral multiple
thereof. Cash will be paid in lieu of any such fraction of an Exchange Debenture
which would otherwise have been issued (which shall be determined with respect
to the aggregate principal amount of Exchange Debentures to be issued to a
holder upon any such exchange). Interest will accrue on the Exchange Debentures
from the date of exchange.

         Prior to effecting any exchange hereunder, the Corporation shall
appoint a trustee to serve in the capacity contemplated by an indenture between
the Corporation and such trustee, containing customary terms and conditions.

         The EXCHANGE RATIO shall be, as of any Dividend Payment Date, $1.00 (or
fraction thereof) of principal amount of Exchange Debenture for each $1.00 of
(i) Liquidation Value plus (ii) accrued and unpaid cash dividends, if any, per

<PAGE>   13
                                                                         Page 13

share of Senior Preferred Stock held by a holder on the applicable exchange
date.

         "AFFILIATES" shall have the meaning ascribed such term in the
Investors' Agreement.

         "EXCHANGE DEBENTURES" means 13% Subordinated Exchange Debentures due
2010 of the Corporation, to be issued pursuant to an indenture between the
Corporation and a trustee, containing customary terms and conditions, in
accordance with the Term Sheet attached as Exhibit A hereto.

         "PERMITTED TRANSFEREES" shall have the meaning ascribed to such term in
the Investors' Agreement.

                  (b) Procedure for Exchange. (i) In the event the Corporation
shall exchange shares of Senior Preferred Stock, notice of such exchange shall
be given by first class mail, postage prepaid, mailed not less than 30 days nor
more than 60 days prior to the exchange date, to each holder of record of the
shares to be exchanged at such holder's address as the same appears on the stock
register of the Corporation; provided that neither the failure to give such
notice nor any defect therein shall affect the validity of the giving of notice
for the exchange of any share of Senior Preferred Stock to be exchanged except
as to the holder to whom the Corporation has failed to give said notice or
except as to the holder whose notice was defective. Each such notice shall
state: (A) the exchange date; (B) the number of shares of Senior Preferred Stock
to be exchanged; (C) the Exchange Ratio; (D) the place or places where
certificates for such shares are to be exchanged for notes evidencing the
Exchange Debentures to be received by the exchanging holder; and (E) that
dividends on the shares to be exchanged will cease to accrue on such exchange
date.

                   (ii) Prior to giving notice of intention to exchange, the
                  Corporation shall execute and deliver with a bank or trust
                  company selected by the Corporation an indenture containing
                  customary terms and conditions. The Corporation will cause the
                  Exchange Debentures to be authenticated on the Dividend
                  Payment Date on which the exchange is effective, and will pay
                  interest on the Exchange Debentures at the rate and on the
                  dates specified in such indenture from the exchange date.

                           The Corporation will not give notice of its intention
                  to exchange under paragraph 6(b)(i) hereof unless it shall
                  file at the place or places (including a place in the Borough
                  of Manhattan, The City of New York) maintained for such
                  purpose an opinion of counsel (who may be an employee of the
                  Corporation) to the effect that (i) the indenture has been
                  duly authorized, executed and delivered by the Corporation,
                  has been duly qualified under the Trust Indenture Act of 1939
                  (or that such qualification is not 

<PAGE>   14
                                                                         Page 14

                  necessary) and constitutes a valid and binding instrument
                  enforceable against the Corporation in accordance with its
                  terms (subject, as to enforcement, to bankruptcy, insolvency,
                  reorganization and other laws of general applicability
                  relating to or affecting creditors' rights and to general
                  equity principles, and subject to such other qualifications as
                  are then customarily contained in opinions of counsel
                  experienced in such matters), (ii) the Exchange Debentures
                  have been duly authorized and, when executed and authenticated
                  in accordance with the provisions of the indenture and
                  delivered in exchange for the shares of Preferred Stock, will
                  constitute valid and binding obligations of the Corporation
                  entitled to the benefits of the indenture (subject as
                  aforesaid), (iii) neither the execution nor delivery of the
                  indenture or the Exchange Debentures nor compliance with the
                  terms, conditions or provisions of such instruments will
                  result in a breach or violation of any of the terms or
                  provisions of, or constitute a default under, any indenture,
                  mortgage, deed of trust or agreement or instrument, known to
                  such counsel, to which the Corporation or any of its
                  subsidiaries is a party or by which it or any of them is
                  bound, or any decree, judgment, order, rule or regulation,
                  known to such counsel, of any court or governmental agency or
                  body having jurisdiction over the Corporation and such
                  subsidiaries or any of their properties, (iv) the Exchange
                  Debentures have been duly registered for such exchange with
                  the Securities and Exchange Commission under a registration
                  statement that has become effective under the Securities Act
                  of 1933 (the "Act") or that the exchange of the Exchange
                  Debentures for the shares of Senior Preferred Stock is exempt
                  from registration under the Act, and (v) the Corporation has
                  sufficient legally available funds for such exchange such that
                  such exchange is permitted under applicable law.

                   (iii) Notice having been mailed as aforesaid, from and after
                  the exchange date (unless default shall be made by the
                  Corporation in issuing Exchange Debentures in exchange for the
                  shares called for exchange), dividends on the shares of Senior
                  Preferred Stock so called for exchange shall cease to accrue,
                  and all rights of the holders thereof as stockholders of the
                  Corporation (except the right to receive from the Corporation
                  the Exchange Debentures and any rights such holder, upon the
                  exchange, may have as a holder of the Exchange Debenture)
                  shall cease. Upon surrender in accordance with said notice of
                  the certificates for any shares so exchanged (properly
                  endorsed or assigned for transfer, if the Board of Directors
                  of the Corporation shall so require and the notice shall so
                  state), such share shall be exchanged by the Corporation for
                  the Exchange Debentures at the Exchange Ratio. In case fewer
                  than all the shares represented by any such certificate are
                  exchanged, a 

<PAGE>   15
                                                                         Page 15


                  new certificate shall be issued representing the unexchanged
                  shares without cost to the holder thereof.

                  (iv) Each exchange shall be deemed to have been effected
                  immediately after the close of business on the relevant
                  Dividend Payment Date, and the person in whose name or names
                  any Exchange Debentures shall be issuable upon such exchange
                  shall be deemed to have become the holder of record of the
                  Exchange Debentures represented thereby at such time on such
                  Dividend Payment Date.

                  (v) Prior to the delivery of any securities which the
                  Corporation shall be obligated to deliver upon exchange of the
                  Senior Preferred Stock, the Corporation shall comply with all
                  applicable federal and state laws and regulations which
                  require action to be taken by the Corporation.

         (c) The Corporation will pay any and all documentary stamp or similar
issue or transfer taxes payable in respect of the issue or delivery of notes
evidencing Exchange Debentures on exchange of the Senior Preferred Stock
pursuant hereto; provided that the Corporation shall not be required to pay any
tax which may be payable in respect of any transfer involved in the issue or
delivery of Exchange Debentures in a name other than that of the holder of the
Senior Preferred Stock to be exchanged and no such issue or delivery shall be
made unless and until the person requesting such issue or delivery has paid to
the Corporation the amount of any such tax or has established, to the
satisfaction of the Corporation, that such tax has been paid.

                  (8) VOTING RIGHTS. (a) The holders of record of shares of
Senior Preferred Stock shall not be entitled to any voting rights except as
hereinafter provided in this paragraph (8), as otherwise provided by law or as
provided in the Investors' Agreement.

                  (b) If and whenever (i) four consecutive or six quarterly cash
dividends payable on the Senior Preferred Stock have not been paid in full, (ii)
for any reason (including the reason that funds are not legally available for a
redemption), the Corporation shall have failed to discharge any Mandatory
Redemption Obligation (including a redemption in the Event of a Change of
Control pursuant to Section 5(c) hereof), (iii) the Corporation shall have
failed to provide the notice required by Section 6(c) hereof within the time
period specified in such section or (iv) the Corporation shall have failed to
comply with Sections 3(d), 3(e) or 8(c) hereof, (1) the number of directors then
constituting the Board of Directors shall be increased by two and the holders of
a majority of the outstanding shares of Senior Preferred Stock, together with
the holders of shares of every other series of preferred stock upon which like
rights have been conferred and are exercisable (resulting from either the
failure to pay dividends or the failure to redeem) (any such series is referred
to as the "PREFERRED 

<PAGE>   16
                                                                         Page 16

SHARES"), voting as a single class regardless of series, shall be entitled to
elect the two additional directors to serve on the Board of Directors at any
annual meeting of stockholders or special meeting held in place thereof, or at a
special meeting of the holders of the Senior Preferred Stock and the Preferred
Shares called as hereinafter provided. Whenever (i) all arrears in cash
dividends on the Senior Preferred Stock and the Preferred Shares then
outstanding shall have been paid and cash dividends thereon for the current
quarterly dividend period shall have been paid or declared and set apart for
payment, (ii) the Corporation shall have fulfilled its Mandatory Redemption
Obligation, (iii) fulfilled its obligation to provide notice as specified in
subsection (b)(iii) hereof, or (iv) the Corporation shall have complied with
Sections 3(d), 3(e), or 8(c) hereof, as the case may be, then the right of the
holders of the Senior Preferred Stock to elect such additional two directors
shall cease (but subject always to the same provisions for the vesting of such
voting rights in the case of any similar future (i) arrearage in six consecutive
quarterly cash dividends, (ii) failure to fulfill any Mandatory Redemption
Obligation, (iii) failure to fulfill the obligation to provide the notice
required by Section 6(d) hereof within the time period specified in such section
or (iv) failure to comply with Sections 3(d), 3(e), or 8(c)) and the terms of
office of all persons elected as directors by the holders of the Senior
Preferred Stock shall forthwith terminate and the number of the Board of
Directors shall be reduced accordingly. At any time after such voting power
shall have been so vested in the holders of shares of Senior Preferred Stock and
the Preferred Shares, the secretary of the Corporation may, and upon the written
request of any holder of Senior Preferred Stock (addressed to the secretary at
the principal office of the Corporation) shall, call a special meeting of the
holders of the Senior Preferred Stock and of the Preferred Shares for the
election of the two directors to be elected by them as herein provided, such
call to be made by notice similar to that provided in the Bylaws of the
Corporation for a special meeting of the stockholders or as required by law. If
any such special meeting required to be called as above provided shall not be
called by the secretary within 20 days after receipt of any such request, then
any holder of shares of Senior Preferred Stock may call such meeting, upon the
notice above provided, and for that purpose shall have access to the stock books
of the Corporation. The directors elected at any such special meeting shall hold
office until the next annual meeting of the stockholders or special meeting held
in lieu thereof if such office shall not have previously terminated as above
provided. If any vacancy shall occur among the directors elected by the holders
of the Senior Preferred Stock and the Preferred Shares, a successor shall be
elected by the Board of Directors, upon the nomination of the then-remaining
director elected by the holders of the Senior Preferred Stock and the Preferred
Shares or the successor of such remaining director, to serve until the next
annual meeting of the stockholders or special meeting held in place thereof if
such office shall not have previously terminated as provided above.

         (c) Without the written consent of a majority of the outstanding shares
of Senior Preferred Stock or the vote of holders of a majority of the
outstanding shares of Senior Preferred Stock at a meeting of the holders of
Senior Preferred Stock called for such purpose, the Corporation will not (i)
amend, alter or repeal any provision of the Certificate of Incorporation (by
merger or otherwise) so as to adversely affect the preferences, rights or powers
of the Senior Preferred Stock; provided that any such amendment that decreases
the dividend payable on or the Liquidation Value of the Senior Preferred Stock
shall require the affirmative vote of holders of each share of Senior Preferred
Stock at a meeting of holders of Senior Preferred Stock called for such purpose
or written consent of the holder of each share of Senior Preferred 
<PAGE>   17

                                                                         Page 17


Stock; or (ii) create, authorize or issue any class of stock ranking prior to,
or on a parity with, the Senior Preferred Stock with respect to dividends or
upon liquidation, dissolution, winding up or otherwise, or increase the
authorized number of shares of any such class or series, or reclassify any
authorized stock of the Corporation into any such prior or parity shares or
create, authorize or issue any obligation or security convertible into or
evidencing the right to purchase any such prior or parity shares, except that
the Corporation may, without such approval, create authorize and issue Parity
Securities for the purpose of utilizing the proceeds from the issuance of such
Parity Securities for the redemption or repurchase of all outstanding shares of
Senior Preferred Stock in accordance with the terms hereof or of the Investors'
Agreement.

         (d) In exercising the voting rights set forth in this paragraph (8),
each share of Senior Preferred Stock shall have one vote per share, except that
when any other series of preferred stock shall have the right to vote with the
Senior Preferred Stock as a single class on any matter, then the Senior
Preferred Stock and such other series shall have with respect to such matters
one vote per $25 of Liquidation Value or other liquidation preference. Except as
otherwise required by applicable law or as set forth herein, the shares of
Senior Preferred Stock shall not have any relative, participating, optional or
other special voting rights and powers and the consent of the holders thereof
shall not be required for the taking of any corporate action.

         (9) REPORTS. So long as any of the Senior Preferred Stock is
outstanding, the Corporation will furnish the holders thereof with the quarterly
and annual financial reports that the Corporation is required to file with the
Securities and Exchange Commission pursuant to Section 13 or Section 15(d) of
the Securities Exchange Act of 1934 or, in the event the Corporation is not
required to file such reports, reports containing the same information as would
be required in such reports.

         (10) GENERAL PROVISIONS. (a) The term "PERSON" as used herein means any
corporation, limited liability company, partnership, trust, organization,
association, other entity or individual.

               (b) The term "OUTSTANDING", when used with reference to shares of
         stock, shall mean issued shares, excluding shares held by the
         Corporation or a subsidiary.

               (c) The headings of the paragraphs, subparagraphs, clauses and
         subclauses used herein are for convenience of reference only and shall
         not define, limit or affect any of the provisions hereof.

               (d) Each holder of Senior Preferred Stock, by acceptance thereof,
         acknowledges and agrees that payments of dividends, interest, premium
         and principal on, and exchange, redemption and repurchase of, such
         securities by the Corporation are subject to restrictions on the
         Corporation contained in certain credit and financing agreements.

               FIFTH: No contract or transaction between the Corporation and one
         or more of its directors, officers, or stockholders or between the
         Corporation and any person (as used herein "person" means any other
         corporation, partnership, association, firm, trust, joint venture,
         political subdivision, or instrumentality) or other organization in
         which one or more of its directors, officers, or stockholders are
         directors, officers or stockholders, or have a financial interest,
         shall be void or voidable solely for this reason, or solely because the
         director or officer is present at or participates in the meeting of the
         board or committee which authorizes the contract or transaction, or
         solely because his, her, or their votes are counted for such purpose,
         if: (i) the material facts as to his or her relationship or interest
         and as to the contract or transaction are disclosed or are known to the
         board of directors or the committee, and the board of directors or
         committee in good faith authorizes the contract or transaction by the
         affirmative votes of a 

<PAGE>   18
                                                                         Page 18

         majority of the disinterested directors, even though the disinterested
         directors be less than a quorum; or (ii) the material facts as to his
         or her relationship or interest and as to the contract or transaction
         are disclosed or are known to the stockholders entitled to vote
         thereon, and the contract or transaction is specifically approved in
         good faith by vote of the stockholders; or (iii) the contract or
         transaction is fair as to the Corporation as of the time it is
         authorized, approved, or ratified by the board of directors, a
         committee thereof (to the extent permitted by applicable law), or the
         stockholders. Common or interested directors may be counted in
         determining the presence of a quorum at a meeting of the board of
         directors or of a committee which authorizes the contract or
         transaction.

               SIXTH: The Board of Directors shall have the power to adopt,
         amend or repeal the bylaws of the Corporation.

               SEVENTH: Election of directors need not be by written ballot
         unless the bylaws of the Corporation so provide.

               EIGHTH: A director of the Corporation shall not be personally
         liable to the Corporation or its stockholders for monetary damages for
         breach of fiduciary duty as a director, except for liability (i) for
         any breach of the director's duty of loyalty to the Corporation or its
         stockholders, (ii) for acts or omissions not in good faith or which
         involve intentional misconduct or knowing violation of law, (iii) under
         Section 174 of the Delaware Law, or (iv) for any transaction from which
         the director derived an improper personal benefit. Any repeal or
         amendment of this Article EIGHTH by the stockholders of the Corporation
         shall be prospective only, and shall not adversely affect any
         limitation on the personal liability of a director of the Corporation
         arising from an act or omission occurring prior to the time of such
         repeal or amendment. In addition to the circumstances in which a
         director of the Corporation is not personally liable as set forth in
         the foregoing provisions of this Article EIGHTH, a director shall not
         be liable to the Corporation or its stockholders to such further extent
         as permitted by any law hereafter enacted, including without limitation
         any subsequent amendment to the Delaware Law.

               NINTH: (1) A director of the Corporation shall not be liable to
         the Corporation or its stockholders for monetary damages for breach of
         fiduciary duty as a director to the fullest extent permitted by
         Delaware Law.

               (2)(a) Each person (and the heirs, executors or administrators of
         such person) who was or is a party or is threatened to be made a party
         to, or is involved in any threatened, pending or completed action, suit
         or proceeding, whether civil, criminal, administrative or
         investigative, by reason of the fact that such person is or was a
         director or officer of the Corporation or is or was serving at the
         request of the Corporation as a director or officer of another
         corporation, partnership, joint venture, trust or other enterprise,
         shall be indemnified and held harmless by the Corporation to the
         fullest extent permitted by Delaware Law. 

<PAGE>   19
                                                                         Page 19

         The right to indemnification conferred in this Article NINTH
         shall also include the right to be paid by the Corporation the expenses
         incurred in connection with any such proceeding in advance of its final
         disposition to the fullest extent authorized by Delaware Law. The right
         to indemnification conferred in this Article NINTH shall be a contract
         right.

               (b) The Corporation may, by action of its Board of Directors,
         provide indemnification to such of the officers, employees and agents
         of the Corporation to such extent and to such effect as the Board of
         Directors shall determine to be appropriate and authorized by Delaware
         Law.

               (3) The Corporation shall have power to purchase and maintain
         insurance on behalf of any person who is or was a director, officer,
         employee or agent of the Corporation, or is or was serving at the
         request of the Corporation as a director, officer, employee or agent of
         another corporation, partnership, joint venture, trust or other
         enterprise against any expense, liability or loss incurred by such
         person in any such capacity or arising out of his status as such,
         whether or not the Corporation would have the power to indemnify him
         against such liability under Delaware Law.

               (4) The rights and authority conferred in this Article NINTH
         shall not be exclusive of any other right which any person may
         otherwise have or hereafter acquire.

               (5) Neither the amendment nor repeal of this Article NINTH, nor
         the adoption of any provision of this Certificate of Incorporation or
         the bylaws of the Corporation, nor, to the fullest extent permitted by
         Delaware Law, any modification of law, shall eliminate or reduce the
         effect of this Article NINTH in respect of any acts or omissions
         occurring prior to such amendment, repeal, adoption or modification.

               TENTH: The Corporation expressly elects not to be governed by
         Section 203 of the Delaware Law.

               ELEVENTH: The Corporation reserves the right to amend this
         Certificate of Incorporation in any manner permitted by Delaware Law
         and, with the sole exception of those rights and powers conferred under
         the above Article NINTH, all rights and powers conferred herein on
         stockholders, directors and officers, if any, are subject to this
         reserved power.
<PAGE>   20
                                                                         Page 20

                                                                       EXHIBIT A



                                SUMMARY OF TERMS
                                OF INDENTURE FOR
                      13% SUBORDINATED EXCHANGE DEBENTURES

<TABLE>

<S>                                <C>
PARTIES:                             Thermadyne Holdings Corporation (the
                                     "CORPORATION") and [            ], as trustee.
ISSUE:                               13% Exchange Debentures (the "EXCHANGE
                                     DEBENTURES") to be issued by the Corporation, at
                                     its option, in exchange for any or all the
                                     outstanding shares of 13% Senior Exchangeable
                                     Preferred Stock due 2010 (the "SENIOR PREFERRED
                                     STOCK") issued on or about May 15, 1998 to DLJ
                                     Merchant Banking Partners II, L.P. and certain of
                                     its affiliates (the "DLJ ENTITIES").
MATURITY:                            May 15, 2010.
INTEREST:                            13% annual rate, payable semi-annually.
                                     Through the semi-annual interest payment period
                                     ending in May 2003, semi-annual interest will
                                     accrete on a compound basis (i.e. non-cash pay)
                                     and increase the face amount of the Exchange
                                     Debentures, thereafter interest will be payable in
                                     cash.
RANKING:                             The Exchange Debentures will rank senior to all
                                     other subordinated debt, preferred stock and
                                     common equity of the Corporation.

OPTIONAL REDEMPTION:                 The Exchange Debentures will be redeemable at
                                     any time after May 15, 2003 at the option of the
                                     Corporation, in whole or in part, at the same
                                     redemption prices set forth in the desigination of
                                     the Senior Preferred Stock set forth in Article
                                     FOURTH, paragraph (c) of the Restated
                                     Certificate of Incorporation of the Surviving
                                     Corporation.
</TABLE>
<PAGE>   21
                                                                         Page 21
<TABLE>


<S>                                <C>
CHANGE OF CONTROL                    In the event of a Change of Control of the
REPURCHASE RIGHT:                    Corporation each holder of the Exchange
                                     Debentures will have the right to require
                                     the Corporation to repurchase all or any
                                     part of such holder's Exchange Debentures
                                     at a purchase price of 101% of the sum of
                                     the accreted value thereof plus accrued and
                                     unpaid cash interest, if any, to the
                                     repurchase date.
COVENANTS:                           The Debentures will contain covenants that are
                                     substantially the same as the covenants contained
                                     in the Indenture of the [ ____ Senior Discount
                                     Debentures due 2008] of the Corporation and will
                                     limit, among other things, the ability of the
                                     Corporation and its subsidiaries (i) to incur
                                     additional indebtedness, (ii) to pay dividends and
                                     make other distributions on its capital stock, (iii)
                                     to repurchase its capital stock or warrants,
                                     options or other rights to acquire shares of its
                                     capital stock or any indebtedness subordinated to
                                     the Exchange Debentures, (iv) to make certain
                                     other restricted payments, (v) to make certain
                                     investments or asset sales, (vi) to engage in
                                     transactions with affiliates, (vii) to create liens,
                                     (viii) to permit "layering" of indebtedness and
                                     (ix) to merge or consolidate or transfer all or
                                     substantially all of its assets."
</TABLE>

<PAGE>   22
                                                                         Page 22

         7. Except as specifically amended by this Amendment, the Agreement
shall remain in full force and effect.

         IN WITNESS WHEREOF, the parties hereto have executed this Amendment to
the Agreement as of this 22nd day of April, 1998.




                                      THERMADYNE HOLDINGS
                                      CORPORATION


                                      By: /s/ RANDALL E. CURRAN
                                         -----------------------------
                                         Name: Randall E. Curran
                                         Title: President



                                      MERCURY ACQUISITION
                                      CORPORATION


                                      By: /s/ WILLIAM F. DAWSON, JR.
                                         -----------------------------
                                         Name: William F. Dawson, Jr.
                                         Title: Vice President