Having hunted in Alaska many times, I can tell you that you are in NO way OVER-GUNNED. If anything you are considering going UNDER-GUNNED. Flags was dead on correct in his assessment. Unless you are well trained with handguns and experienced "under fire" you do NOT want to meet up with Big Brown with that .44mag in your hand. Nor do you want to try one on in a surprise "greeting" with a bolt action rifle. I can tell you in no uncertain terms that an aggressive Female Brown with cubs just coming out of Hibernation with one or two cubs can and will end your greeting in a BAD way. When Trout fishing you will want to have a good 12 gauge loaded up just like Flags proposed. Spring and early summer can create a deadly scenario in some areas. Some people promote Bear Spray and while yes it will work, it has to be under proper conditions. If the wind is in your face, all you are going to do is add a little pepper flavor to Big Browns meal. Now usually a Brown will leave you alone if they come up on you at a stream or something like that, but a surprise crossing or as I said ANY female with cubs to protect will assault you if you are close.
As far as hunting, goes, May you can get some spring bear in. Come mid August you will have a large variety of animals to go for from Whitetail to Moose according to what GMU you will be in.