I was just in Alaska on May 26th - June 3rd. First I can say enough how great Alaska really is, it's breathtaking.
As for clothing, I packed a (Wisconsin) fall jacket, wore those stretchy gloves you can get for a 1.00 (12.00 on the ship) and a baseball cap. I only wore that when we were going through Tracey Arm and were outside on the deck. During the town excurisons I wore a heavy sweatshirt, and I was comfortable.
I would definitely dress in layers, long sleeve t-shirt, sweatshirt.
I really didn't bring that many articles of clothing, I was ready to purchase some alaskan shirts.
Have a wonderful trip.