You aren't being placed in the FBI database because you are a veteran.  It is because you own a gun.  If you don't want to be in the database, don't own a gun.

However, even these rules seem awfully lax to me:
http://www.hawaiipolice.com/services/firearm-registration

BTW, when you joined the military you had to submit to an SF87 fingerprint card.  The VA asks you to fill it out also.   Where do you think this information is stored?  So it isn't like your privacy is being breached by these Hawaii Laws.  The FBI pages will tell you how to submit one.