Hi Bridget,
May can be a complicated time of year for Alaska, though typically much of the snow and ice is gone, especially in the more accessible areas. Certainly in the higher elevations there may still be a bit of snow and the weather will be cooler, but you can typically expect daytime temperatures averaging 15 degrees, but at night things are still quite a bit cooler with temperatures averaging 3-5 degrees.
As you mentioned, layers are the general rule so you can easily adjust to current weather conditions for maximum comfort. Unless you plan on hiking anywhere, you're not likely to have to worry about the snow and ice. Even a late-season snowfall will only last a short time and the places you visit on the trip will have paths and outdoor staircases cleared immediately.
As for dress code, there is no where for which you should be concerned about being underdressed. As always, comfort and practicality are the highest priority, so just wear something you will feel relaxed and warm in.
There are now 17 people booked on this trip and with ages ranging from the early-40's to the late-70's, you'll have a blast.
I hope this helps.
Kindest regards,
Monty