I do a fair amount of backpacking and other wilderness adventures alone. It's where a lot of my healing takes place, and as some of you may know, I'm writing a book about my PTSD, my journey, and healing in the wilderness. However, I strive to get as far away from people as I can.
As Yogi Bear said "The deeper into the woods ya' get, the more nuts ya' find."
Which is of course true in more than one sense. I think wilderness draws sufferers of civilization for its ability to heal us. I think heavily wooded, poorly patrolled places where people go often draws criminals. I recommend going out farther, away from the crowds, where it gets really wild. That's where you'll feel the most legitimate fear, of real dangers, not triggers, and you'll never feel more alive.
If you've read the book Wild by Cheryl Strayed, there's a passage where she encounters two bowhunters, one of which became aggressive toward her. For my part, I've only been scared of people once, when two guys got into my personal space. They have miles and miles to stand in, but they were two feet from me. At that moment, I wish I was carrying because I know they were. One of them, clearly an idiot, said he had felt threatened by a black bear and considered getting out his pistol. Now if you know anything about black bears in the Sierras, just yelling is enough to send them scurrying.
So...long story short. The farther out into the wilderness you go, I'd say you are generally safer than in town. That said, I would recommend the large cans of pepper spray called Bear .... something. They have been proven to work on grizzly bears, so they will work on the more dangerous two-legged predators. I honestly feel that most people would hesitate to shoot, unless you have combat experience and know what you would do if a situation arose. With non-lethal pepper spray, I don't think you would. And for the love of Dog, if you do go way out there, please get some training so that you know what to do in case of emergency. I now carry an Emergency Locator Beacon.
As for carrying or packing heat in a national park, it is illegal to carry a firearm unless there are specific rules that state otherwise, like if its hunting season. As for designated wilderness areas (see the US Wilderness Act of 1964), the laws in that area of the state are pertinent. Most of the time, you can openly carry, but you can't pack the thing in your pack because that's concealed and therefore illegal. Do not take this at face value; I could be wrong. Check your local laws.
I used to carry out in the bush, but it wasn't for protection really. Back when I was seriously suicidal, I took a .44 with me. And then the beauty of the place got to me and what do you know, I'm still here.