Rain in Alaska tends to be drizzle, not heavy rain. Drizzle can be a downer, but if you expect it, then the sunshine in between can be a real treat!
That's how we saw it. It rained much, but not all, of the day in Ketchikan for us, and several other days of our 10-day cruise, and we went in May. Southeast Alaska is wet, no question about it, but downpours and even full days of steady rain are highly unusual.