I've been to Alaska a number of times, driving/riding 'naked' in every case. Never broke into a sweat, never even though about it actually.
I suspect I'd have had a far greater chance of a run in with someone texting while driving, than any situation that demanded "personal protection".
Mail your firearm to yourself in AK, last I checked that was totally legal. Or leave it with a pal somewhere near the border and don't tell no one!
Enjoy your ride in the Canadian interior, and into Alaska, nothing like it in the world. At least by bike from the lower 48 anyway
Rick