<PAGE>   1
 
                             LETTER OF TRANSMITTAL
                                   TO TENDER
            UNREGISTERED 12 1/2% SENIOR DISCOUNT DEBENTURES DUE 2008
                                       OF
 
                        THERMADYNE HOLDINGS CORPORATION
       PURSUANT TO THE EXCHANGE OFFER AND PROSPECTUS DATED AUGUST 4, 1998
 
THE EXCHANGE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., NEW YORK CITY
TIME, ON SEPTEMBER 3, 1998 (THE "EXPIRATION DATE"), UNLESS THE EXCHANGE OFFER IS
EXTENDED BY THE COMPANY.
 
                 THE EXCHANGE AGENT FOR THE EXCHANGE OFFER IS:
 
                       IBJ SCHRODER BANK & TRUST COMPANY
 
                                   Deliver to
               IBJ Schroder Bank & Trust Company, Exchange Agent
 
<TABLE>
<S>                             <C>                             <C>
  By Registered or Certified         By Overnight Courier:             By Hand Delivery:
             Mail:                 IBJ Schroder Bank & Trust       IBJ Schroder Bank & Trust
   IBJ Schroder Bank & Trust                Company                         Company
            Company                    One State Street                One State Street
          P.O. Box 84              New York, New York 10004        New York, New York 10004
     Bowling Green Station        Attn: Securities Processing     Attn: Securities Processing
 New York, New York 10274-0084   Window, Subcellar One, (SC-1)   Window, Subcellar One, (SC-1)
Attn: Reorganization Operations Facsimile Transmission Number:
          Department              (For Eligible Institutions
                                             Only)
                                        (212) 858-2103
                                Confirm Receipt of Facsimile by
                                          Telephone:
                                        (212) 858-2611
</TABLE>
 
    (Originals of all documents sent by facsimile should be sent promptly by
   registered or certified mail, by hand, or by overnight delivery service.)
 
     DELIVERY OF THIS LETTER OF TRANSMITTAL TO AN ADDRESS OR TRANSMISSION OF
INSTRUCTIONS VIA FACSIMILE OTHER THAN AS SET FORTH ABOVE WILL NOT CONSTITUTE A
VALID DELIVERY.
 
     IF YOU WISH TO EXCHANGE UNREGISTERED 12 1/2% SENIOR DISCOUNT DEBENTURES DUE
2008, FOR AN EQUAL AGGREGATE PRINCIPAL AMOUNT OF REGISTERED 12 1/2% SENIOR
DISCOUNT DEBENTURES DUE 2008, PURSUANT TO THE EXCHANGE OFFER, YOU MUST VALIDLY
TENDER (AND NOT WITHDRAW) OLD DEBENTURES TO THE EXCHANGE AGENT PRIOR TO THE
EXPIRATION DATE.
 
                          SIGNATURES MUST BE PROVIDED.
              PLEASE READ THE ACCOMPANYING INSTRUCTIONS CAREFULLY.
<PAGE>   2
 
                     DESCRIPTION OF TENDERED OLD DEBENTURES
 
<TABLE>
<S>                                                           <C>                  <C>
------------------------------------------------------------------------------------------------------
       NAME(S) AND ADDRESS(ES) OF REGISTERED OWNER(S)             CERTIFICATE           AGGREGATE
AS IT APPEARS ON THE 12 1/2% SENIOR DISCOUNT DEBENTURES DUE        NUMBER(S)        PRINCIPAL AMOUNT
                            2008                                    OF OLD          OF OLD DEBENTURES
                 (PLEASE FILL IN, IF BLANK)                       DEBENTURES            TENDERED
------------------------------------------------------------------------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
                                                                TOTAL PRINCIPAL
                                                                 AMOUNT OF OLD
                                                                  DEBENTURES
                                                                   TENDERED
------------------------------------------------------------------------------------------------------
</TABLE>
<PAGE>   3
 
LADIES AND GENTLEMEN:
 
     1. The undersigned hereby tenders to Thermadyne Holdings Corporation, a
Delaware corporation (the "Company"), the 12 1/2% Senior Discount Debentures due
2008 (the "Old Debentures"), described above pursuant to the Company's offer of
$1,000 principal amount of 12 1/2% Senior Discount Debentures due 2008 (the "New
Debentures"), in exchange for each $1,000 principal amount of the Old
Debentures, upon the terms and subject to the conditions contained in the
Prospectus dated August 4, 1998 (the "Prospectus"), receipt of which is hereby
acknowledged, and in this Letter of Transmittal (which together constitute the
"Exchange Offer").
 
     2. The undersigned hereby represents and warrants that it has full
authority to tender the Old Debentures described above. The undersigned will,
upon request, execute and deliver any additional documents deemed by the Company
to be necessary or desirable to complete the tender of Old Debentures.
 
     3. The undersigned understands that the tender of the Old Debentures
pursuant to all of the procedures set forth in the Prospectus will constitute an
agreement between the undersigned and the Company as to the terms and conditions
set forth in the Prospectus.
 
     4. Unless the box under the heading "Special Registration Instructions" is
checked, the undersigned hereby represents and warrants that:
 
          (i) the New Debentures acquired pursuant to the Exchange Offer are
     being obtained in the ordinary course of business of the undersigned,
     whether or not the undersigned is the holder;
 
          (ii) neither the undersigned nor any such other person is engaging in
     or intends to engage in a distribution of such New Debentures;
 
          (iii) neither the undersigned nor any such other person has an
     arrangement or understanding with any person to participate in the
     distribution of such New Debentures; and
 
          (iv) neither the holder nor any such other person is an "affiliate,"
     as such term is defined under Rule 405 promulgated under the Securities Act
     of 1933, as amended (the "Securities Act"), of the Company.
 
     5. The undersigned may, if, and only if, unable to make all of the
representations and warranties contained in Item 4 above, elect to have its Old
Debentures registered in the shelf registration described in the Exchange and
Registration Rights Agreement, dated as of May 22, 1998, between the Company and
the Initial Purchaser in the form filed as an exhibit to the Registration
Statement (the "Registration Agreement") (all terms used in this Item 5 with
their initial letters capitalized, unless otherwise defined herein, shall have
the meanings given them in the Registration Agreement). Such election may be
made by checking the box under "Special Registration Instructions" on page 5. By
making such election, the undersigned agrees, as a holder of Transfer Restricted
Securities participating in a shelf registration, to indemnify and hold harmless
the Company, its directors and officers and each person, if any, who controls
the Company within the meaning of either Section 15 of the Securities Act or
Section 20 of the Securities Exchange Act of 1934, as amended (the "Exchange
Act"), from and against any and all losses, claims, damages, liabilities and
judgments (including, without limitation, any legal or other expenses incurred
in connection with defending or investigating any matter), joint or several, or
any action in respect thereof, to which the Company or any such director,
officer or controlling person may become subject, under the Securities Act or
otherwise, insofar as such loss, claim, damage, liability or action arises out
of, or is based upon (i) any untrue statement or alleged untrue statement of a
material fact contained in the Shelf Registration Statement or the Prospectus or
in any amendment or supplement thereto, (ii) or the omission or alleged omission
to state therein a material fact required to be stated therein or necessary to
make the statements therein not misleading, but only with reference to such
information relating to the undersigned furnished in writing by or on behalf of
the undersigned expressly for use in the Shelf Registration Statement, the
Prospectus or any amendments or supplements thereto. Any such indemnification
shall be governed by the terms and subject to the conditions set forth in the
Registration Agreement, including, without limitation, the provisions regarding
notice, retention of counsel, contribution and payment of expenses set forth
therein. The above summary of the
<PAGE>   4
 
indemnification provision of the Registration Agreement is not intended to be
exhaustive and is qualified in its entirety by the Registration Agreement.
 
     6. If the undersigned is not a broker-dealer, the undersigned represents
that it is not engaged in, and does not intend to engage in, a distribution of
New Debentures. If the undersigned is a broker-dealer that will receive New
Debentures for its own account in exchange for Old Debentures that were acquired
as a result of market-making activities or other trading activities, it
acknowledges that it will deliver a prospectus in connection with any resale of
such New Debentures; however, by so acknowledging and delivering a prospectus,
the undersigned will not be deemed to admit that it is an "underwriter" within
the meaning of the Securities Act. If the undersigned is a broker-dealer and Old
Debentures held for its own account were not acquired as a result of
market-making or other trading activities, such Old Debentures cannot be
exchanged pursuant to the Exchange Offer.
 
     7. Any obligation of the undersigned hereunder shall be binding upon the
successors, assigns, executors, administrators, trustees in bankruptcy and legal
and personal representatives of the undersigned.
 
     8. Unless otherwise indicated herein under "Special Delivery Instructions,"
the certificates for the New Debentures will be issued in the name of the
undersigned.
 
                         SPECIAL DELIVERY INSTRUCTIONS
                              (See Instruction 1)
 
     To be completed ONLY IF the New Debentures are to be issued or sent to
someone other than the undersigned or to the undersigned at an address other
than that provided above.
 
        Mail [ ]  Issue [ ]  (check appropriate boxes) certificates to:
 
Name:
--------------------------------------------------------------------------------
                                 (PLEASE PRINT)
 
Address:
--------------------------------------------------------------------------------
 
       -------------------------------------------------------------------------
 
       -------------------------------------------------------------------------
                              (INCLUDING ZIP CODE)
 
                       SPECIAL REGISTRATION INSTRUCTIONS
                                  (See Item 5)
 
     To be completed ONLY IF (i) the undersigned satisfies the conditions set
forth in Item 5 above, (ii) the undersigned elects to register its Old
Debentures in the shelf registration described in the Registration Agreement,
and (iii) the undersigned agrees to indemnify certain entities and individuals
as set forth in the Registration Agreement and summarized in Item 5 above.
 
     [ ] By checking this box the undersigned hereby (i) represents that it is
unable to make all of the representations and warranties set forth in Item 4
above, (ii) elects to have its Old Debentures registered pursuant to the shelf
registration described in the Registration Agreement, and (iii) agrees to
indemnify certain entities and individuals identified in, and to the extent
provided in, the Registration Agreement and summarized in Item 5 above.
<PAGE>   5
 
                       SPECIAL BROKER-DEALER INSTRUCTIONS
                                  (See Item 6)
 
     [ ] Check here if you are a broker-dealer and wish to receive 10 additional
copies of the Prospectus and 10 copies of any amendments or supplements thereto.
 
Name:
--------------------------------------------------------------------------------
                                 (PLEASE PRINT)
 
Address:
--------------------------------------------------------------------------------
 
       -------------------------------------------------------------------------
 
       -------------------------------------------------------------------------
                              (INCLUDING ZIP CODE)
<PAGE>   6
 
--------------------------------------------------------------------------------
 
                                   SIGNATURE
 
        To be completed by all exchanging debentureholders. Must be signed by
   registered holder exactly as name appears on Old Debentures. If signature
   is by trustee, executor, administrator, guardian, attorney-in-fact,
   officer of a corporation or other person acting in a fiduciary or
   representative capacity, please set forth full title. See Instruction 3.
 
   X
   --------------------------------------------------------------------------
 
   X
   --------------------------------------------------------------------------
          SIGNATURE(S) OF REGISTERED HOLDER(S) OR AUTHORIZED SIGNATURE
 
   Dated:
   --------------------------------------------------------------------------
 
   Name(s):
   --------------------------------------------------------------------------
 
   --------------------------------------------------------------------------
                             (PLEASE TYPE OR PRINT)
 
   Capacity:
   --------------------------------------------------------------------------
 
   Address:
   --------------------------------------------------------------------------
 
   --------------------------------------------------------------------------
 
   --------------------------------------------------------------------------
                              (INCLUDING ZIP CODE)
 
   Area Code and Telephone No.:
 
 -------------------------------------------------------------------------------
 
               SIGNATURE GUARANTEE (IF REQUIRED BY INSTRUCTION 1)
 
        Certain Signatures Must be Guaranteed by an Eligible Institution
 
   --------------------------------------------------------------------------
             (NAME OF ELIGIBLE INSTITUTION GUARANTEEING SIGNATURES)
 
   --------------------------------------------------------------------------
    (ADDRESS (INCLUDING ZIP CODE) AND TELEPHONE NUMBER (INCLUDING AREA CODE)
                                    OF FIRM)
 
   --------------------------------------------------------------------------
                             (AUTHORIZED SIGNATURE)
 
   --------------------------------------------------------------------------
                                 (PRINTED NAME)
 
   --------------------------------------------------------------------------
                                    (TITLE)
 
   Dated:
   --------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
                      PLEASE READ THE INSTRUCTIONS BELOW,
                WHICH FORM A PART OF THIS LETTER OF TRANSMITTAL.
<PAGE>   7
 
                                  INSTRUCTIONS
 
     1. GUARANTEE OF SIGNATURES. Signatures on this Letter of Transmittal must
be guaranteed by an eligible guarantor institution that is a member of or
participant in the Securities Transfer Agents Medallion Program, the New York
Stock Exchange Medallion Signature Program or by an "eligible guarantor
institution" within the meaning of Rule 17Ad-15 promulgated under the Exchange
Act (an "Eligible Institution") unless the box entitled "Special Registration
Instructions" or "Special Delivery Instructions" above has not been completed or
the Old Debentures described above are tendered for the account of an Eligible
Institution.
 
     2. DELIVERY OF LETTER OF TRANSMITTAL AND OLD DEBENTURES. The Old
Debentures, together with a properly completed and duly executed Letter of
Transmittal (or copy thereof), should be mailed or delivered to the Exchange
Agent at the address set forth above.
 
     THE METHOD OF DELIVERY OF OLD DEBENTURES AND THE LETTER OF TRANSMITTAL AND
ALL OTHER REQUIRED DOCUMENTS TO THE EXCHANGE AGENT IS AT THE ELECTION AND RISK
OF THE HOLDER. INSTEAD OF DELIVERY BY MAIL, IT IS RECOMMENDED THAT HOLDERS USE
AN OVERNIGHT OR HAND DELIVERY SERVICE. IN ALL CASES, SUFFICIENT TIME SHOULD BE
ALLOWED TO ASSURE DELIVERY TO THE EXCHANGE AGENT BEFORE THE EXPIRATION DATE. NO
LETTER OF TRANSMITTAL OR OLD DEBENTURES SHOULD BE SENT TO THE COMPANY. HOLDERS
MAY REQUEST THEIR RESPECTIVE BROKERS, DEALERS, COMMERCIAL BANKS, TRUST
COMPANIES, OR NOMINEES TO EFFECT THE ABOVE TRANSACTIONS FOR SUCH HOLDERS.
 
     3. SIGNATURE ON LETTER OF TRANSMITTAL, BOND POWERS AND ENDORSEMENTS. If
this Letter of Transmittal is signed by a person other than a registered holder
of any Old Debentures, such Old Debentures must be endorsed or accompanied by
appropriate bond powers, signed by such registered holder exactly as such
registered holder's name appears on such Old Debentures.
 
     If this Letter of Transmittal or any Old Debentures or bond powers are
signed by trustees, executors, administrators, guardians, attorneys-in-fact,
officers of corporations, or others acting in a fiduciary or representative
capacity, such persons should so indicate when signing, and, unless waived by
the Company, proper evidence satisfactory to the Company of their authority to
so act must be submitted with this Letter of Transmittal.
 
     4. MISCELLANEOUS. All questions as to the validity, form, eligibility
(including time of receipt), acceptance, and withdrawal of tendered Old
Debentures will be determined by the Company in its sole discretion, which
determination will be final and binding on all parties. The Company reserves the
absolute right to reject any or all Old Debentures not properly tendered or any
Old Debentures the Company's acceptance of which would, in the opinion of
counsel for the Company, be unlawful. The Company also reserves the right to
waive any defects, irregularities, or conditions of tender as to particular Old
Debentures. The Company's interpretation of the terms and conditions of the
Exchange Offer (including the instructions in this Letter of Transmittal) will
be final and binding. Unless waived, any defects or irregularities in connection
with tenders of Old Debentures must be cured within such time as the Company
shall determine. Neither the Company, the Exchange Agent, nor any other person
shall be under any duty to give notification of defects in such tenders or shall
incur any liability for failure to give such notification. Tenders of Old
Debentures will not be deemed to have been made until such defects or
irregularities have been cured or waived. Any Old Debentures received by the
Exchange Agent that are not properly tendered and as to which the defects or
irregularities have not been cured or waived will be returned by the Exchange
Agent to the tendering holder thereof as soon as practicable following the
Expiration Date.