I dug into this recently flying to Vegas, I was trying to avoid checking a bag as I was flying standby, it's very easy for your bags to make it without you when you fly standby. but it is difficult legally to get a gun to your destination any other way than checked luggage if you are flying. closest i found was to send it to a trusted party in your name, they cannot open the package but i did not have anyone to send it to.
I have flown to Anchorage several times with firearms, never really an issue, just takes a bit more time, check the airlines website, for restrictions, for instance last time I flew there was a max of 11 pounds of ammo and it had to be well packaged, the original retail packaging was sufficient. The case had to have a lock. Etc etc I will echo the caveats of connecting flights in certain blue states, they will arrest you.
when you get to the ticket counter to check your bags tell them you need to declare a firearm and follow instructions. They will put piece of paper inside the bag and a gun tag outside.
Last time I flew they never looked at the gun, they took my word for it and just did the paper work, but about 10 years ago I had a ticket agent that wanted me to cycle the action was kinda weird in the middle of an airport but was no issue.
They always tell me to follow the bag to TSA as they may want to open the case also but TSA has never wanted to. they x-ray it, see the gun they were already expecting and move on.
Bears are rarely a problem, they know you are there long before you know they are there and will generally avoid you, although still rare your chances of being bear poop increase dramatically when you are in thier fishing areas with a backpack full of fish. Bears have better sense of smell than dogs or even deer, We carried shotguns with slugs, brown bears are tough. In several trips to Alaska I only saw bears once and they were on the other side of the river! The best way to see a bear in person!
Open carry in AK is not a problem with the law. My buddy made friends with a colorful local, he made a living carving wooden bears with a chainsaw and selling them on the side of the road. From sun up to sun down he was always drinking but never visibly intoxicated. we went fishing with him he had a beer in one hand, a joint in the other and a shotgun slung over his shoulder we were at a popular fishing spot on federal land, a fish and wildlife officer walked by, waved hello and kept on walking. I am no advocate of using drugs and alcohol while handling firearms but the Libertarian in me found it to be an interesting moment of complete freedom.
I did not and would not open carry in Anchorage, your shinny colt will look like pill money to someone. concealed would be preferable in more populated areas. IMO.
We were also witness to a fatal head on collision while there. the driving distances are huge and even on a main highway it took a long time for rescue crews to get there and longer still to extract one of the injured survivor. Everyone stopped and many tried to help but without power equipment we could not do much besides wait, Be careful you are far from help in many parts of AK.