Unless the city of Arlington has more stringent regulations than the state of VA regarding firearms ownership (and I THOUGHT that VA has state-level pre-emption of local regulations, but could be mistaken or Arlington could have been grandfathered for pre-existing regulations), there is no permit required for firearms ownership. Buy a gun from a private seller, and the .gov has no involvement at all. Or you could buy a deactivated or blank-firing firearm, which look visually-identical to the real deal and should require the same sort of inspection with no possibility of requiring a Form 4473 from the seller. Not sure whether a part alone would do the job.

That's a great idea, IMO, to ensure you'll be there when TSA rifles through your luggage. Then too, it'd take up one of your checked-bag allotments. Perhaps a handgun case inside a larger checked suitcase?

Disclaimer: IANAL, just a firearms and civil-rights enthusiast.