Bags of medication? (perhaps containing "asthma inhalers" of anthrax, tear gas?)
Baby supplies?
What length of flight will you allow something to be carried?
What about a back brace? (something someone has noted, you could take a gun apart and hide it in a back brace, something that's never checked by airport security)....
Just not a real solution there, either. Cutting down on it would be a good idea, but you won' tbe able to not have it.
Don't forget the "shuttle" flights where nobody checks baggage.
Addison