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I'm a serious deep-country backpacker in north-western Canada. We have grizzly, black bear, cougar, and moose here. I have had encounters with all of them. Most notably, I was within a few FEET of a cougar during one winter trip. I was in my hammock half asleep when he approached. I was petrified when I noticed him at my feet. I didn't move, I didn't blink, I didn't breathe. Eventually he slowly wandered off and left me alone. This is the only time in over twenty years of camping that I have ever felt in danger.
Now, I'm also a licensed gun owner and an avid hunter. I have a respectable collection of firearms.
I do not carry any of my guns while I am backpacking. I know what it's like to lug a heavy gun and ammo around all day while hunting, and I do not want to do that while I'm scaling a mountain or traversing a rock field. I believe a gun would be an unnecessary hindrance. It would likely just end up inside my pack, out of reach. Do you really want to traverse boulders with a shotgun in your hand? No? So what good is it?
If you really feel uncomfortable / unsafe in the back country, it sounds to me like you have no business being there to begin with. Put a gun in a nervous man's hand, and you have trouble.
TL;DR - Guns are unnecessary. Be smart about where you cook, don't empty bacon grease beside your tent, don't gut fish near camp, and you'll be fine. This is coming from someone who has thousands of miles of hiking and countless hunts in the Canadian far-north under his belt - not some armchair commando - and I hope that counts for something.
If you *really* want ideas, pic related is what I carry on a hunt. The shotgun is a Stoeger Outback, and it breaks in half then goes inside my backpack while I'm hiking to my hunting grounds.Very packable.