It is impossible to predict the weather in Alaska anytime. We cruised the inside passage about 6 years ago during the second week in Sept, and the weather was great! Clear skies and temp's in the 60's every day. Talked to some people in Juneau and they said it was the best weather they had had for a year.
My suggestion is to expect rain and cooler weather and if you get sun and warmer weather it's a bonus!! We are going on the Spirit on 9/11 and that is what we will be doing. Rain gear and layers of cloths which are easy to remove WHEN it warms up.
Have a great trip!! I am sure you will no matter what the weather is.