Headstamps and rifles don't very often kill things. Bullets do, though. All you "Get a Magnum" guys ever have wives or children that you goaded with that same horseshit, or were the size of your testicles sufficient in those times to simply hand them the rifle that would be honestly enough? I promise: EVERYONE shoots small cartridges better in sporting-weight rifles.
The "magnum" thing means nothing. For example, a .458 Lott shoots big testicles, but does not have a "magnum" on the head-stamp. Yes, the OP can use any of the numerous small cartridges to hunt caribou, because these animals aren't very large (from 300-400 pounds, which leaves about 100 pounds of meat). All kinds of small cartridges have been used for decades to kill caribou in Alaska. But it's true that there is a good chance to have bears (black and grizzly) where the caribou are.
By the way, the caribou hunting season in the Interior of Alaska has been quite nice. Lots of people got their caribou. For some reason I don't like to hunt nor eat caribou meat, but love moose meat. The moose season starts in a little over a week from now.
