We went to alaska a few years ago in August. We actually had wonderful weather compared to what is "usual". In Skagway and Ketchikan, it was sunny, and we could have worn shorts and a light jacket. I freeze easily, so I always had a jacket and pants, but my teenagers wore shorts. On those days, they also went in the pool and hot tubs. they were heated on our cruise (NCL SKy). Cruising through the glaciers it was drizzling and chilly. I had on rain coat over a polartec jacket and was wishing i had gloves! I don't know about anything in the water other than deep sea fishing. There might be some scuba type thing. You should be able to get a list of shore excursions offered by your ship.
Take the swimsuit, take shorts, but also take pants, rain jacket and sweatshirts. Have fun!