The old Savage 24 combo models had many shotgun/rifle caliber choices, but they were pretty heavy and didn’t breakdown. There were many other combo guns, some light, most heavy available.
You might want to consider a big bore handgun. A Super Redhawk .454 Casull will take anything you want. You could launch .45 wadcutters and take small game with little damage. You could scope it or not. You just wouldn’t have a shotgun abaility. And it weighs about 52 oz and will fit in your pack.
I though about a hand gun, and I have several.
But on the Appalachian Trail, you go through Pennsylvania, New Jersey, New York, Connecticut; Vermont, New Hampshire, and Maine.
Most of those states aren't "hand gun friendly"
and I just don't want to deal with the hassle of getting my pack checked and explaining Mississippi's gun permits.
Also, there's the danger of a mother bear defending her cubs.
The extra barrel length of a 16" to 18" rifle might be worth the extra weight.