Oh how fun, Sarah! My family took a cruise to Alaska two summers ago and it was so cool! You're right to prepare for cooler temperatures; we went in August but still needed warm layers. Most cruise lines are pretty casual these days, but there are also some more upscale ones, so some of this depends on what cruise line you travel with. I'll assume the more mainstream casual ones for my suggestions.
What surprised me and left me a bit unprepared was how chilly it was on the boat itself, in the inside rooms. The air conditioning was on very high, and I constantly grabbed cardigans and other layers even on days where we were able to use the pool outside! So I'd make sure to assume layering inside even on hot days.
The weather we encountered on sea and in Alaska was very mixed. There were several days where we could hang out on deck in bathing suits, and hike in tank tops and shorts when on shore, but then there were also chillier days. So again, layers layers layers are key. I'd pick some "formula" like jeans (full length and/or clamdiggers), nice tank/sleeveless blouse, plus cardigan, as your standard attire. That will work both on the boat and on shore.
For evenings, you can then dress it up as much as you'd like. I found that evening attire ranged from jeans to dressy, so you have lots of options. I'd take a couple nice dresses or skirt/top ensembles, but again, make sure you have layers (like cardigans) that work with them, since you will rarely feel like going sleeveless on the boat. Flats or heels will work at night, whatever floats your boat (ha!).
Comfortable footwear is a must, especially for your shore excursions. We did some basic hikes, for which fashion sneakers were totally appropriate. If you do something more rugged, you need actual gear. I'd also take comfortable sandals, something that's as comfy as Birkenstocks but looks better I think there've been a lot of threads on the forum about this last summer, maybe you can dig something up.
Very important: A good wind and rain jacket. We actually only had rain once on the boat, but it was windy a lot, so if you want to spend time out on deck on the chillier days, you absolutely need a good jacket that breaks the wind. I'd look at actual "gear" for that in an outdoor sporting goods store - they still come in nice colors if you're lucky
Have fun!!!
