<PAGE>   1
                                                                   EXHIBIT 10.23


                                                                          Page 1

                                 Award Agreement
                                    under the
                         Thermadyne Holdings Corporation
                            Management Incentive Plan



                  Date of Grant:            May 22, 1998

                  Name of Optionee:         James H. Tate

                  Number of Shares
                    Time Vesting:           25,843
                    Cliff Vesting:          25,843

                  Exercise Price:           $34.50/share

                  Expiration Date:          May 22, 2008


         Thermadyne Holdings Corporation, a Delaware corporation (the
"COMPANY"), hereby grants to the above-named optionee (the "OPTIONEE") a time
vesting option (the "TIME VESTING OPTION") and a cliff vesting option (the
"CLIFF VESTING OPTION" and, together with the Time Vesting Option, the
"OPTIONS") to purchase from the Company, for the price per share set forth
above, the number of shares of Common Stock, $0.01 par value (the "SHARES"), of
the Company set forth above pursuant to the Thermadyne Holdings Corporation
Management Incentive Plan (the "PLAN"). The Options are not intended to be
treated as incentive stock options under the Code.

         Capitalized terms not otherwise defined herein shall have the same
meanings as in the Plan. The terms and conditions of the Option granted hereby,
to the extent not controlled by the terms and conditions contained in the Plan,
are as follows:

         1. Exercise Price. The price at which each Share subject to this Option
may be purchased shall be the price set forth above.

         2. Number of Shares; Exercise. The number of Shares for which the Time
Vesting Option and the Cliff Vesting Option may be exercised are set forth
above. To the extent this Option has become vested in accordance with Sections 3
and 4 below, the Option may be exercised at any time until the Expiration Date,
subject to the terms of the Plan and of Section 8 below.

<PAGE>   2
                                                                          Page 2

         3. Vesting: Time Vesting Option. As of the Date of Grant, the Time
Vesting Option shall become vested and exercisable with respect to 20% of the
Shares subject thereto. On each of the first five anniversaries of the Date of
Grant, provided the Optionee is then in the employ of the Company or a
Subsidiary, the Time Vesting Option shall become vested and exercisable with
respect to an additional 16% of the Shares subject thereto.

         4. Vesting: Cliff Vesting Option.

         (a) To the extent not previously vested in accordance with paragraph
(b) or (c) below, the Cliff Vesting Option shall become fully vested and
exercisable on the eighth anniversary of the Date of Grant, provided the
Optionee is then in the employ of the Company or a Subsidiary.

         (b) The Cliff Vesting Option shall become vested and exercisable with
respect to 20% of the Shares subject thereto on the thirtieth day following the
availability of audited financial statements for each of the five fiscal years
of the Company commencing with the fiscal year ending December 31, 1998 (each
such day a "CLIFF VESTING DATE"), provided the implied common equity value of
the Company as of the end of such fiscal year, calculated in accordance with
Exhibit A hereto, is at least equal to the target value for such fiscal year set
forth in such Exhibit A, and provided further that the Optionee is in the employ
of the Company or a Subsidiary on such Cliff Vesting Date. If the target set
forth in Exhibit A for any of the first four fiscal years referred to above is
not attained, the portion of the Cliff Vesting Option that would otherwise have
vested for such fiscal year shall be treated as vested and exercisable as of the
Cliff Vesting Date for any subsequent fiscal year ending on or before December
31, 2002 for which the target for such subsequent year is attained, provided the
Optionee is in the employ of the Company or a Subsidiary on such Cliff Vesting
Date.

         (c) Upon the occurrence of a Liquidation Event, provided the DLJ
Entities' realized annual investment rate of return as calculated in accordance
with Exhibit B ("DLJ IRR") is at least 20%, and provided the Optionee is in the
employ of the Company or a Subsidiary as of such Liquidation Event, the Cliff
Vesting Option shall become vested and exercisable with respect to a portion of
the Shares subject thereto as to which the Option has not yet vested in
accordance with paragraph (b) above ("UNVESTED CLIFF VESTING SHARES"). In such
case, the Cliff Vesting Option will become vested and exercisable with respect
to the applicable percentage of the Unvested Cliff Vesting Shares set forth in
Exhibit B hereto, based on the DLJ IRR.

         5. Manner of Exercise. The Optionee (or his representative, devisee or
heir, as applicable) may exercise any portion of this Option which has become
exercisable in accordance with the terms hereof as to all or any of the Shares
then available for purchase by delivering to the Company written notice
specifying:
<PAGE>   3
                                                                          Page 3

                  (i) the number of whole Shares to be purchased together with
         payment in full of the aggregate Exercise Price of such shares;

                  (ii) the address to which dividends, notices, reports, etc.
         are to be sent; and

                  (iii) the Optionee's social security number.

Payment shall be in cash, by certified or bank cashier's check payable to the
order of the Company, free from all collection charges, or in unencumbered
Shares (provided such shares shall have been held by the Optionee for at least
six months unless the Committee determines in its sole discretion that such
six-month holding period is not necessary to comply with any accounting, legal
or regulatory requirement) having a Fair Market Value equal to the full amount
of the Exercise Price therefor, or such other form as may be permitted by the
Committee. Only one stock certificate will be issued unless the Optionee
otherwise requests in writing. Shares purchased upon exercise of the Option will
be issued in the name of the Optionee or the Optionee's Permitted Transferee.
The Optionee shall not be entitled to any rights as a stockholder of the Company
in respect of any Shares covered by this Option until such Shares shall have
been paid for in full and issued to the Optionee.

         6. Certificates. Certificates issued in respect of Shares acquired upon
exercise of the Option shall, unless the Committee otherwise determines, be
registered in the name of the Optionee or its Permitted Transferee. When the
Optionee ceases to be bound by the provisions of the Investors' Agreement, the
Company shall deliver such certificates to the Optionee or its Permitted
Transferee upon request. Such stock certificate shall carry such appropriate
legends, and such written instructions shall be given to the Company's transfer
agent, as may be deemed necessary or advisable by counsel to the Company in
order to comply with the requirements of the Securities Act of 1933, any state
securities laws or any other applicable laws or the Investors' Agreement.

         7. Nontransferability. This Option is personal to the Optionee and may
be exercised only by the Optionee or his or her representative in the event of
the Optionee's Disability or death. This Option shall not be transferable other
than by will or the laws of descent and distribution. Notwithstanding the
foregoing, this Option may be transferred to a trust solely for the benefit of
the Optionee or the Optionee's immediate family (which shall be deemed to
include the Optionee's spouse, parents, siblings, children, stepchildren and
grandchildren).

         8.        Forfeiture of Option; Right of Repurchase.

<PAGE>   4
                                                                          Page 4

         (a) If the Optionee's employment with the Company and its Subsidiaries
shall terminate for any reason other than by the Company or its Subsidiary for
Cause, then (i) to the extent not yet vested as of the date of termination of
employment, the Option shall immediately be forfeited; and (ii) to the extent
vested as of the date of termination of employment, the Option may be retained
and exercised, in accordance with the terms of the Plan and this Award
Agreement, until the Expiration Date.

         (b) If the Optionee's employment with the Company and its Subsidiaries
shall be terminated by the Company or its Subsidiary for Cause, then the entire
Option shall immediately be forfeited, and all Shares previously acquired upon
exercise of the Option shall be subject to a right of repurchase by the Company
from the Participant or his or her Permitted Transferee at a price equal to the
Exercise Price.

         9. Change of Control. Upon a Change of Control, the Time Vesting Option
shall vest in its entirety and become immediately exercisable and, if the Change
of Control constitutes a Liquidation Event, the Cliff Vesting Option shall vest
in accordance with Section 4(c) hereof.

         10. Sale of Underlying Shares. The Optionee's right to sell any Shares
acquired upon exercise of the Option (in the case of Optionees who are party
thereto) shall be subject to the terms of the Investors' Agreement.

         11. Employment Rights. This Option does not confer on the Optionee any
right to continue in the employ of the Company or any Subsidiary or interfere in
any way with the right of the Company or any Subsidiary to determine the terms
of the Optionee's employment.

         12. Terms of Plan; Interpretations. This Option and the terms and
conditions herein set forth are subject in all respects to the terms and
conditions of the Plan, which shall be controlling. All interpretations or
determinations of the Committee and/or the Board shall be binding and conclusive
upon the Optionee and his legal representatives on any question arising
hereunder. The Optionee acknowledges that he has received and reviewed a copy of
the Plan.

         13. Delegation. Optionee acknowledges that any powers, rights or
responsibilities of the Board and/or the Committee set forth herein may be
delegated to and exercised by any subcommittee thereof as permitted under the
Plan.

<PAGE>   5
                                                                          Page 5

         14. Notices. All notices hereunder to the party shall be delivered or
mailed to the following addresses:

                  If to the Company:

                  Thermadyne Holdings Corporation
                  c/o DLJ Merchant Banking Partners II, L.P.
                  277 Park Avenue
                  New York, New York  10172
                  Attention: Peter T. Grauer
                  Fax: (212) 892-7272

                  and

                  Thermadyne Holdings Corporation
                  101 South Hanley Road
                  St. Louis, Missouri  63105
                  Attention:  James H. Tate and Stephanie N. Josephson
                  Fax:  (314) 746-2374

                  with a copy to:

                  Davis Polk & Wardwell
                  450 Lexington Avenue
                  New York, New York  10017
                  Attention: George R. Bason, Jr.
                  Fax:  (212) 450-4800

                  If to the Optionee:

                  To the person and at the address specified on the signature
                  page.

Such addresses for the service of notices may be changed at any time provided
notice of such change is furnished in advance to the other party.

         15. Entire Agreement. This Agreement, together with the Plan and (in
the case of Optionees who are party thereto) the Investors Agreement, contains
the entire understanding of the parties hereto in respect of the subject matter
contained herein. This Agreement, the Plan and (in the case of Optionees who are
party thereto) the Investors' Agreement supersede all prior agreements and
understandings between the parties hereto with respect to the subject matter
hereof.

         16. Governing Law. This Award Agreement shall be governed by and
construed in accordance with the laws of the State of Delaware, without
application of the conflict of laws principles thereof.

         17. Counterparts. This Award Agreement may be signed in any number of
counterparts, each of which shall be an original, with the same effect as if the
signatures thereto and hereto were upon the same instrument.

<PAGE>   6
                                                                          Page 6

         IN WITNESS WHEREOF, the undersigned have caused this Award Agreement to
be duly executed as of the date first above written.

                                       THERMADYNE HOLDINGS
                                       CORPORATION


                                       By: /s/ STEPHANIE N. JOSEPHSON
                                           -------------------------------------
                                           Name:
                                           Title:


                                       OPTIONEE:

                                          /s/ JAMES H. TATE
                                       -----------------------------------------
                                       Name:  James H. Tate
                                       Address:  c/o Thermadyne Holdings Corp.
                                                     101 South Hanley Road
                                                     St. Louis, Missouri 63105