We went to Alaska in August, so I'm not sure if the weather is different. But we were very fortunate during the whole cruise. We may have had a little sprinkle in Ketchikan, but that was the extend of any rain. It was sunny most port days. Our tour guide in Skagway mentioned that they received heavy rain for the past few days including the day before we arrived. It was so bad that one of the ships couldn't dock. But as soon as we arrived, it was sunny and warm. I believed him. On our way to the train excursion, the area looked like it was just flooded.
You can't predict the weather, in a matter of hours it could be raining heavy or misting or sunny. As long pp mentioned, as long as you're prepared, you'll enjoy your trip.