I live outside Fairbanks. The most cruises I see coming through are Princess (you fly into the Fairbanks International Airport and then bus to the port in Valdez). They aren't overly dressy. Here is the site for Princess' Alaskan cruises.
In general, Alaska is pretty informal. It's also cold down in Southeast, even in the summer. I'd be surprized if anyone was wearing anything other than jeans and a flannel.
Hope this helps!
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