Typically, if the shuttle is equipped with seat belts, like a 15-18 passenger van, then you will need a car seat. If the shuttle does not have seat belts, like the vans often used by car rental agencies, then you will not need the car seat.
The airline will check the car seat for free if you choose not to use it on your flight. Bringing your own car seat will open up many more transportation options. You will not need a car seat if you use the cruise line bus to get to the port.