Personally, I wouldn't carry a handgun in the field if I were carrying a rifle. I do like having one in the tent at night, if the tent is small. The odds of a bear bothering you are slim and I probably wouldn't worry about bringing a handgun if I were you. You will be flying out to hunt and weight is always an issue, besides flying all the way to Alaska with it. If you do, I think the 10mm is fine. That's what I keep in my tent when I'm by myself (Delta Elite). If my wife is along, she carries a 44mag (329).
I will say that with you going way up north, above the Arctic circle, the interior Arctic grizzlies tend to be more aggressive than the coastal brown bears. They don't enjoy the big runs of salmon and have to mostly eat berries or kill stuff to get their nutrition. They are smaller but meaner, in my opinion and experience. Not as many of them though.