Calf:
My Alaska cruise was over 10 years ago, but even with Global Warming, I don't think the weather has changed much. When I cruised there in August, I had packed a light winter jacket, ear muffs, rain jacket and gloves. Nothing went unused. May and September are the chilliest months to cruise Alaska, but that does not deter from the magnificent beauty that awaits you. Be prepared for chilly weather, but also for warmth. The daily ship life is quite different from a Caribbean cruise, as they may not even fill the pools for the voyage (they didn't on my ship), and most of the day is spent along the railings sightseeing. It can get a little brisk, if you are dressed in shorts and a T-shirt!
My advice would be to pack for both conditions, and that way you are completely prepared for whatever you encounter. You will be enchanted by this cruise. Mine provided me with breathtaking photos and a lifetime of memories!
Enjoy your cruise, as I know you will.