I think non-americans need to get off the ship in between, you need to clear customs/immigration again.
CC is about 15 minutes from the port, we pulled in and saw the price (about $120 for the 4 of us) and decided against it, our children are small and we didn't feel that they would enjoy it. I'm sure a taxi would be pretty inexpensive.
If you get off last and just hang out you should be back on board within a couple of hours. Hope that helps.