We did exactly that in 2014. Left Prince Rupert in mid-May. Then:
--2 nights in Ketchikan
--3 nights on Prince of Wales Island (Got there via Inter-Island ferry.)
--2 more nights in Ketchikan
--4 nights in Sitka (Our favorite place in our 8 weeks in BC/Alaska.)
--1 night in Juneau (Got there from Sitka via the fast ferry. Ferry system was down by one boat so we had to leave earlier than we wanted.)
--Arrived in Haines. (Didn't go to Skagway. Save that for later.)
We played around a lot with the departure date and got civilized departure and arrival times. We needed a room only for the Ketchikan-Sitka leg. The other legs were in the daylight hours.