You could do several things. Reserve you a room over at the Raddison or the Holiday Inn in Cocoa Beach. When you land, have a car service company pick you up and transfer you to the hotel in CB. If you want you can book a hotel close to the Orlando airport for the night, use their airport shuttle and have a car service pick you up at the hotel and take you to the Port the next day around 1000. The same car service should offer a roundtrip price to return and pick you up and deliver you to MCO when your boat redocks. Don't use a one way car service you will end up paying more. The service that might take you to the hotel should be able to come back and pick you up when the boat docks.
The hotels at the Beach (Raddison for sure) have shuttles to the boat. It is about 1 1/2 miles to the dock from the Raddison, but they may have high rates. You can check the Port Canaveral website for companies that are licensed to pick you up over there. I would call those companies and set up a roundtrip passage. The website for the port is portcanaveral.org and I will check for sure on that.
A website taxi-mco.com has a listing of drivers who are permitted to take you to the port and return you. You might check that out.