<PAGE>   1
 
                             LETTER OF TRANSMITTAL
                                   TO TENDER
             UNREGISTERED 9 7/8% SENIOR SUBORDINATED NOTES DUE 2008
                                       OF
 
                              THERMADYNE MFG. LLC
                                      AND
 
                            THERMADYNE CAPITAL CORP.
       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:
 
                      STATE STREET BANK AND TRUST COMPANY
 
                                  Deliver to:
              State Street Bank and Trust Company, Exchange Agent
 
<TABLE>
<S>                                             <C>
      By Registered or Certified Mail:                      By Hand (in Boston):
        State Street Bank and Trust                     State Street Bank and Trust
                  Company                                         Company
                P.O. Box 778                              Two International Place
        Boston, Massachusetts 02102                    Fourth Floor, Corporate Trust
      Attn: Corporate Trust Department                  Boston, Massachusetts 02110
               Kellie Mullen                               By Hand (in New York):
           By Overnight Courier:                        State Street Bank and Trust
        State Street Bank and Trust                            Company, N.A.
                  Company                                 61 Broadway, 15th Floor
          Two International Place                          Corporate Trust Window
        Boston, Massachusetts 02110                       New York, New York 10006
      Attn: Corporate Trust Department
               Kellie Mullen
                                     Telephone Number:
                                       (617) 664-5587
</TABLE>
 
     DELIVERY OF THIS LETTER OF TRANSMITTAL TO AN ADDRESS OTHER THAN AS SET
FORTH ABOVE WILL NOT CONSTITUTE A VALID DELIVERY.
 
     IF YOU WISH TO EXCHANGE UNREGISTERED 9 7/8% SENIOR SUBORDINATED NOTES DUE
2008, FOR AN EQUAL AGGREGATE PRINCIPAL AMOUNT OF REGISTERED 9 7/8% SENIOR
SUBORDINATED NOTES DUE 2008, PURSUANT TO THE EXCHANGE OFFER, YOU MUST VALIDLY
TENDER (AND NOT WITHDRAW) OLD NOTES 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 NOTES
 
<TABLE>
<S>                                                           <C>                  <C>
------------------------------------------------------------------------------------------------------
       NAME(S) AND ADDRESS(ES) OF REGISTERED OWNER(S)                                   AGGREGATE
 AS IT APPEARS ON THE 9 7/8% SENIOR SUBORDINATED NOTES DUE        CERTIFICATE       PRINCIPAL AMOUNT
                            2008                                   NUMBER(S)          OF OLD NOTES
                 (PLEASE FILL IN, IF BLANK)                      OF OLD NOTES           TENDERED
------------------------------------------------------------------------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
 
                                                              ------------------------------------
                                                                TOTAL PRINCIPAL
                                                                 AMOUNT OF OLD
                                                                NOTES TENDERED
------------------------------------------------------------------------------------------------------
</TABLE>

<PAGE>   3
 
LADIES AND GENTLEMEN:
 

     1. The undersigned hereby tenders to Thermadyne Mfg. LLC, a Delaware
limited liability company, and Thermadyne Capital Corp., a Delaware corporation
(collectively, the "Issuers"), the 9 7/8% Senior Subordinated Notes due 2008
(the "Old Notes"), described above pursuant to the Issuers' offer of $1,000
principal amount of 9 7/8% Senior Subordinated Notes due 2008 (the "New Notes"),
in exchange for each $1,000 principal amount of the Old Notes, 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 Notes described above. The undersigned will, upon
request, execute and deliver any additional documents deemed by the Issuers to
be necessary or desirable to complete the tender of Old Notes.
 
     3. The undersigned understands that the tender of the Old Notes pursuant to
all of the procedures set forth in the Prospectus will constitute an agreement
between the undersigned and the Issuers 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 Notes 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 Notes;
 
          (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 Notes; 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 Issuers.
 

     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
Notes registered in the shelf registration described in the Exchange and
Registration Rights Agreement, dated as of May 22, 1998, between the Issuers,
the Guarantors 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 Issuers and the Guarantors, their directors and officers and
each person, if any, who controls the Issuers or the Guarantors 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 Issuers or Guarantors, 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


<PAGE>   4
 
of expenses set forth therein. The above summary of the 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 Notes. If the undersigned is a broker-dealer that will receive New Notes for
its own account in exchange for Old Notes 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 Notes;
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 Notes held for its
own account were not acquired as a result of market-making or other trading
activities, such Old Notes 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 Notes will be issued in the name of the
undersigned.
 
                         SPECIAL DELIVERY INSTRUCTIONS
                              (See Instruction 1)
 
     To be completed ONLY IF the New Notes 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 Notes 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 Notes 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.
 
<TABLE>
<S>       <C>
Name:
          ------------------------------------------------------------
                                 (PLEASE PRINT)
Address:
          ------------------------------------------------------------
          ------------------------------------------------------------
          ------------------------------------------------------------
                              (INCLUDING ZIP CODE)
</TABLE>
<PAGE>   6
 
                                   SIGNATURE
 
     To be completed by all exchanging noteholders. Must be signed by registered
holder exactly as name appears on Old Notes. 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 Notes described above are tendered for the account of an Eligible
Institution.
 
     2. DELIVERY OF LETTER OF TRANSMITTAL AND OLD NOTES. The Old Notes, 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 NOTES 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 NOTES 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 Notes, such Old Notes 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 Notes.
 
     If this Letter of Transmittal or any Old Notes 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 Issuers,
proper evidence satisfactory to the Issuers 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 Notes
will be determined by the Issuers in their sole discretion, which determination
will be final and binding on all parties. The Issuers reserve the absolute right
to reject any or all Old Notes not properly tendered or any Old Notes the
Issuers' acceptance of which would, in the opinion of counsel for the Issuers,
be unlawful. The Issuers also reserve the right to waive any defects,
irregularities, or conditions of tender as to particular Old Notes. The Issuers'
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 Notes
must be cured within such time as the Issuers shall determine. Neither the
Issuers, 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 Notes will not be deemed to
have been made until such defects or irregularities have been cured or waived.
Any Old Notes 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.