You certainly do not need to purchase any kind of ships excursion to go to Paradise Island. It can be walked (depending on your idea of a walk),It is not a short stroll.
Water taxis, if you can call them that, run frequently from an area near the ships. They usually wait until they are somewhat full until they leave. For a few dollars per person you get a nice ride of about 10 minutes. Sometimes you will get a little "tour" offered by one of the crew, and occaisionally someone will come and sing a song or two for tips. This is definately the way to go.
Yes, you can get a water taxi or a regular taxi right by the pier. We actually did a ship tour that included a harbor tour and the tour of Atlantis all for $25, not bad and definately worth it. If you want to get into Atlantis and see the aquarium and the area they call the "digs" you will need to purchase some kind of tour, its definately a place to see at least once, have fun!