It will be fine. The weather will be from mid 60s to mid 80s that time of year.
We've done two Alaska cruises, both in late May, and the weather was fabulous. Believe it or not, it can be better then than in July/August.
The first time we were in Ketchikan, rain capital of the world, and there was a sign on a store window, " 11 days in a row with no rain!"
Have fun.
