Avis has an office in the Raddison near the port, and Hertz, National and Budget all have Cocoa Beach offices.
I know that they all have shuttles or reimburse cab rides to get you from the ship to their office, but I don't know for sure about dropping off the car and then getting to the ship.
You could drop off the rest of your group at the port, and have one person return the car. The worst case scenario would be to have to pay for a cab ride back to the port.
Just FYI -- it depends on how many are in your group, but... We are staying 2 days at WDW before the cruise and we were going to take the
DCL bus from the airport to WDW and from WDW to the ship. Then we were going to rent a car for one day (we have a late flight on debarkation day) to sight-see get back to the airport.
We found out that we could rent a minvan for the whole week and park it at the port ($10/day) for what it was going to cost us to take the DCL bus twice and rent it for 1 day (there are 6 of us.)
Alamo has a $189/wk minivan special for the time we will be there. When we started looking, the cheapest we could find was $259/week. We kept checking the codes on mousesavers.com and it helped us find better rates!
Good luck!