We went in early September and had wonderful weather, even sunshine & 70's in Ketchikan. Rain had been forecast for our week, and the weeks & after, had tons of rain. I agree that you must be prepared for alot of rain in September. There were less people & ships still in Alaska, which was great, but alot the tours were closing up for the season. There were alot of great sales on souvineers.
If there is anything specific that you want to do or see, that might dictate the time to travel. More snow & baby animals in May, for example, but we were able to get close to glacier with many baby seals, that was closed until September to protect the baby seals.
Juneau has some great whale watching tours. Skagway has some wonderful trips to the Yukon (by rental car, bus, train or bus/train combo).