I'd amend that by suggesting you take the boat to swan/dolphin, as that's the first boat stop from HS. Then take the bus from Swan/dolphin to DTD.
You should also consider just taking a bus to one of the DTD resorts (Saratoga, Old Key West, or Port Orleans) and taking one of their boats to DTD.
If your feet are up to it, I'd say bus to Saratoga and foot to DTD is the fastest way to get there without taking a taxi