I've done quite a lot of this, but not to Alaska. But, that was 6 years ago. It may have changed.
So, check it out.
Back then, one had to take it to a licensed gun dealer. The gun dealer would send it to a licensed gun dealer at the destination. The gun could then be retrieved from the dealer, by the owner. It was expensive, as both dealers and the shipping merchant got a fee. You had to pass a background check, to pick up your gun, both ends. There is also a fee for that.
As I said, this was years ago. It may have changed.
Ray D.
Consider renting one in Alaska. Then, simply return it before coming back to the lower 48.