We just took our son on his second cruise (he was 14 months). We did the Disney Dream to Nassau and Castaway because we had the same concerns. Having been in several cabs and excursion vans with less than safe driving we had no desire to take the little guy on an excursion because there was no way we were going to lug a car seat around.
We just did a walking tour ourselves of Nassau. We originally planned to spend the day at the Hilton but it was windy and the water was rough even in the port.
My number tip for cruising with infants - bring Grandma