Bottom line up front: Yes, there is an exemption for military qualifications.
From Hawaii Revised Statutes 134-2:
"§134-2 Permits to acquire.
(a) No person shall acquire the ownership of a firearm, whether usable or unusable, serviceable or unserviceable, modern or antique, registered under prior law or by a prior owner or unregistered, either by purchase, gift, inheritance, bequest, or in any other manner, whether procured in the State or imported by mail, express, freight, or otherwise, until the person has first procured from the chief of police of the county of the person's place of business or, if there is no place of business, the person's residence or, if there is neither place of business nor residence, the person's place of sojourn, a permit to acquire the ownership of a firearm as prescribed in this section. When title to any firearm is acquired by inheritance or bequest, the foregoing permit shall be obtained before taking possession of a firearm; provided that upon presentation of a copy of the death certificate of the owner making the bequest, any heir or legatee may transfer the inherited or bequested firearm directly to a dealer licensed under section 134-31 or licensed by the United States Department of Justice without complying with the requirements of this section.
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(g) Effective July 1, 1995, no person shall be issued a permit under this section for the acquisition of a pistol or revolver unless the person, at any time prior to the issuance of the permit, has completed:
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(4) A firearms training or safety course or class conducted by a state certified or National Rifle Association certified firearms instructor
or a certified military firearms instructor that provides, at a minimum, a total of at least two hours of firing training at a firing range and a total of at least four hours of classroom instruction, which may include a video, that focuses on:
(A) The safe use, handling, and storage of firearms and firearm safety in the home; and
(B) Education on the firearm laws of the State.
An affidavit signed by the certified firearms instructor who conducted or taught the course, providing the name, address, and phone number of the instructor and attesting to the successful completion of the course by the applicant shall constitute evidence of certified successful completion under this paragraph."
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