I don't know squat about handguns and their potential to kill (other than a .38 Special on a mountain lion), but I must ask: you realize as a non-resident you need to draw to hunt bear on POW don't you? From the sounds of your post you're making me think that you're assuming it is a registration or hunt ticket hunt. The spring 2022 application period is open right now FYI....and this isn't a real high odds draw. It's not a unicorn tag, but not an unlimited tag either.

I personally wouldn't carry a handgun as backup, even when not primarily bear hunting. Black bears (or even griz) are rarely aggressive especially in spring, though they can be if you're near their food source. I'd be more inclined to carry a .22 LR pistol while fishing for any grouse that want to show up, if they're in season when you're there. Birds there may close on April 30th...I'm not too sure.