The ferry that goes from Bellingham to Skagway takes about 3 days which would save you a little time. I would get off at Haines, however, as the ferry stops there before Skagway and it puts you farther along the Alaksa Highway, west of Whitehorse instead of east. The ferry can be expensive depending on the size of your rig and you should make reservations.
The ferry though the Inside Passage is a nice experience as we have gone from Prince Rupert to Haines on the ferry.
I guess my biggest concern is that the trip to Alaska is such a wonderful adventure it is sad to rush it. That is why I suggested flying and spending the whole time in Alaska rather than spending it driving across the country.