Just got back from Coral Princess. Don't overpack. Remember the people who choose Alaska are not fashion queens. They are people who enjoy nature and are fairly active. I brought 2 pairs of capris but only wore one. Most of the time people wore jeans. Dinner time can be as casual as you want. I wore knit pants one night a denium skirt one night and capris one night. There might be times when you go to the 24 hour buffet which is quite good and then you will probably wear shorts. It is a lot more casual than people think. Some older people really dressed up for the formal night but a simple black dress works. Jogging suits work too. They are comfortable and the jackets come in handy if it is cool on deck. I brought hat and gloves but never wore them. If it is really cold on deck Princess has plaid blanket wraps they will give you.
Some Princess ships have a coin laundry so t-shirts can be washed. Like I said do not over pack. Alaska shopping is great. Shirts are beautiful. Don't forget flip flops and give yourself a treat go to the spa. It was great.