We went on an alaska trip last year in May & the weather was beautiful, but at every port we were told how lucky we were, "It's usually raining". We took ( & some stuff was left unused) hats, scarves & gloves, thermals, pullovers & the like, fleeces & anoracks. And suncream! get to do the White Pass Railway in Skagway, it's very good with great scenery.
For June, we took lightweight sailing macs with hoods, lightweight leather jackets, T shirts and some cashmere pullovers. When necessary, we layered up. I don't think you will need thermals or gloves just prepare for some rain and enjoy!!