You will still need layers in Alaska even in August. We went last June and in the cool breeze you might even need a heavy coat. I brought sweats, windbreakers, vests ect. You may need a parka or several layers if you are going to be doing any excursions that involve glaciers. It is kind of like standing in an ice box.
Also, remember that the Inside Passage area is a rain forrest, so you'll need a raincoat too. Hats of some kind are often practical. Layers are often a better option than a heavy coat because the sun can come out and things can warm up in a hurry.
Don't forget to bring suitible clothes for your ships dining rooms if you plan to do any formal nights. If not , you still might want to bring nice skirts or slacks depending your cruise line's requirements for the more casual nights.