If you are going to hike the nature trails and walk through the woods plus up and down hills, I give you one day carrying that shotgun.
I used to hunt deer with an Ithaca Model 37
Not bad to carry around all day.
An ounce of lead at 1500 FPS is pretty good, but...
I'd be tempted to go with a .338 or bigger if guiding and backing up a client or if on overwatch while quartering an animal in grizzly country.
For casual hiking, I'd go with a handgun.
I have a S&W 629 6" 44 magnum and a Glock G20 10mm
Both are very accurate and easy to shoot.
For hiking in griz country, I'd take my chances with the G20 in a chest rig loaded with either Underwood or Buffalo Bore bear loads.