I wouldn't do it without getting reservations first. You can probably get a shuttle at the "taxi/limo" stand without one, but why risk it? We are doing one way car rentals. You pick the rental up at the airport and drop it off in Port Canavreal. The rental place has a constant shuttle to and from the port. The cost of a minvan one way was less than half of what the cruise line was going to charge for their service. Other options are pre-arranged limo/shuttles if you don't want to deal with the rental. But I would not do it without a reservation.
Yes, a single rental is out of the question. I have a family of four and it will be tight in the minivan I am renting. Try Mears Transportation, they are in Orlando and offer shuttle bus type service. They have been recommended by others here. But I would get a quote from them and compare that against what the cruise line charges. Have a good trip!