Yes - you can get there by a regular taxi. It is not a very long drive at all. You do NOT need a water taxi and that would be a terrible waste of money - although it could be done. The cruise dock is connected to the mainland where the airport is by bridges, it is on the same piece of land as the railroad station.
Ask around so you don't get taken. Ask the locals how much they pay to get to the railroad station - it should not be a significantly higher price.
(All locals go from the airport to the train station if they plan to catch the Vaporetto, it is the closet stop to the airport).