Obviously this only works on domestic flights but the airline will not lose your luggage if they know they are dealing with a legally declared gun. If they do, they get sued by the ATF. Your luggage will be given first priority if you just throw a shitty cheap gun from Walmart in there.
I find that if you get carryon luggage at the exact size of the limit (there's bags advertised as that) + a laptop bag as your personal item you can easily fit enough stuff for a 5 day trip.
If you're staying at a nicer hotel at any point on your trip, the cost of laundry service will probably be less than a checked bag fee if needed.