Unless you are on the beach,you should have "real clothes" on the islands. I take a pair of pull-on shorts (light weight nylon) and a tshirt, and just pull them over my suit. You could also bring a knit sun dress, and throw that over top of your suit.
Overall, for the 7 day, I agree with the suggestions for evening wear as a minimum. For me, I took a pair of white slacks and several summer sweaters to pair with it (I really don't like black, but you do have to worry about spilling something on the white). Add maybe 2 pair of regular shorts, 1 pair of light weight shorts, a couple of t shirts, and you're set. There are laundry rooms on board if you run short of clothes. For me, I lived in my Tevas, and never wore my tennis shoes. I had a pair of slide sandals that I wore for dinner most nights, and a pair of heels for formal/semi-formal night.
Enjoy!