You must be aware of this:
From Wiki:
Prudhoe Bay is the unofficial northern terminus of the Pan-American Highway. The Bay itself is still 10 miles further north than a security checkpoint so open water is not visible from the highway. A few tourists, arriving by bus after a two-day ride up the Dalton Highway from Fairbanks, come to see the tundra, the Arctic Ocean, and the midnight sun, staying in lodgings assembled from modular buildings. Tours must be arranged in advance to see the Arctic Ocean and the Bay itself.
So, ummm, why?
I've seen a couple posts here and on other boards on that problem of packing past gun free zones like Canada to Alaska, including by boat. (Hunters, of course, will fly up there anyhow.)
IIRC, the most practical thing was to ship it to a dealer up there and pick it up when you get there. I recall passages about flying up to Alaska in a chartered (non-TSA) airline, but that's expensive too, and I'm not sure that's a valid method any more.
In any case,
as a practical matter, I think it's fairly safe to transit Canada without a gun anyhow.
I suppose it's possible that new international arrangements for transiting Canada have been made, but I don't know of any.