The Appalachian Trail runs from Georgia to Maine. Could you maybe be just a TAD more specific?
Some of it is in National Parks, much of it on private property. Some is in gun friendly states, some not.
When I do stretches of the AT in Virginia, I carry a sidearm. I have a CCW and can legally do that even in National Parks (a lot of the AT in VA in in Shenandoah National Park). The shotgun you may have an issue with, since no hunting is permitted in a National Park, and the Rangers DO have a problem with poachers.
BTW, my biggest concern on at AT is predators with 2 legs, not 4.