Karen I have sailed Alaska 4 times so far and I did not find it any less formal than sailing through the Panama Canal or sailing Hawaii. I am not sure how people figure it is less formal than the Caribbean. I did not see any less tuxedos or formal gowns than I did on the Mercury through the Canal.
The one thing you do see different is during the day. You will not see all the shorts and swim suits. Of course if you are like me and from the cold country you will see us in shorts and swim suits LOL.