<PAGE>   1
 
                         NOTICE OF GUARANTEED DELIVERY
                                   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
    
 
   
     As set forth in the Prospectus (as defined below), this form or one
substantially equivalent hereto must be used to accept the Exchange Offer if
certificates for unregistered 12 1/2% Senior Discount Debentures due 2008 (the
"Old Debentures"), of Thermadyne Holdings Corporation, are not immediately
available or time will not permit a holder's Old Debentures or other required
documents to reach the Exchange Agent on or prior to the Expiration Date (as
defined below), or the procedure for book-entry transfer cannot be completed on
a timely basis. This form may be delivered by facsimile transmission, by
registered or certified mail, by hand, or by overnight delivery service to the
Exchange Agent. See "The Exchange Offer -- Procedures for Tendering" in the
Prospectus.
    
 
   
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
 
   
<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
          P.O. Box 84                  One State Street                One State Street
     Bowling Green Station         New York, New York 10004        New York, New York 10004
 New York, New York 10274-0084    Attn: Securities Processing     Attn: Securities Processing
Attn: Reorganization Operations  Window, Subcellar One, (SC-1)   Window, Subcellar One, (SC-1)
          Department            Facsimile Transmission Number:
                                  (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 NOTICE TO AN ADDRESS OR TRANSMISSION OF INSTRUCTIONS VIA
FACSIMILE OTHER THAN AS SET FORTH ABOVE WILL NOT CONSTITUTE A VALID DELIVERY.
<PAGE>   2
 
Ladies and Gentlemen:
 
   
     The undersigned hereby tenders to Thermadyne Holdings Corporation, a
Delaware corporation (the "Company"), in accordance with the Company's offer,
upon the terms and subject to the conditions set forth in the Prospectus dated
August 4, 1998 (the "Prospectus"), and in the accompanying Letter of
Transmittal, receipt of which is hereby acknowledged, $     in aggregate
principal amount of Old Debentures pursuant to the guaranteed delivery
procedures described in the Prospectus.
    
 
Name(s) of Registered Holder(s):
---------------------------------------------------------------------
                             (PLEASE TYPE OR PRINT)
 
Address:
--------------------------------------------------------------------------------
 
--------------------------------------------------------------------------------
 
Area Code & Telephone No.:
---------------------------------------------------------------------------
 
Certificate Number(s) for
Old Debentures (if available):
--------------------------------------------------------------------------
 
Total Principal Amount
Tendered and Represented
by Certificate(s): $
--------------------------------------------------------------------------------
 
Signature of Registered Holder(s):
---------------------------------------------------------------------
 
Dated:
--------------------------------------------------------------------------------
 
[ ]  The Depository Trust Company
    (Check if Old Debentures will be tendered
    by book-entry transfer)
 
Account Number:
--------------------------------------------------------------------------------
 
   
                THE GUARANTEE ON THE NEXT PAGE MUST BE COMPLETED
    
<PAGE>   3
 
                                   GUARANTEE
                    (NOT TO BE USED FOR SIGNATURE GUARANTEE)
 
     The undersigned, being a member firm of a registered national securities
exchange, a member of the National Association of Securities Dealers, Inc., or a
commercial bank or trust company having an office in the United States, hereby
guarantees (a) that the above named person(s) "own(s)" the Old Debentures
tendered hereby within the meaning of Rule 14e-4 ("Rule 14e-4") under the
Securities Exchange Act of 1934, as amended, (b) that such tender of such Old
Debentures complies with Rule 14e-4, and (c) to deliver to the Exchange Agent
the certificates representing the Old Debentures tendered hereby or confirmation
of book-entry transfer of such Old Debentures into the Exchange Agent's account
at The Depository Trust Company, in proper form for transfer, together with the
Letter of Transmittal (or facsimile thereof), properly completed and duly
executed, with any required signature guarantees and any other required
documents, within three New York Stock Exchange trading days after the
Expiration Date.
 
   Name of Firm:
   --------------------------------------------------------------------------
 
   Address:
   --------------------------------------------------------------------------
 
   --------------------------------------------------------------------------
 
   Area Code and Telephone No.:
 
 -------------------------------------------------------------------------------
 
   Authorized Signature:
   --------------------------------------------------------------------------
 
   Name:
   --------------------------------------------------------------------------
 
   Title:
   --------------------------------------------------------------------------
 
   Dated:
   --------------------------------------------------------------------------
 
NOTE: DO NOT SEND CERTIFICATES OF OLD DEBENTURES WITH THIS FORM. CERTIFICATES OF
      OLD DEBENTURES SHOULD BE SENT ONLY WITH A LETTER OF TRANSMITTAL.