We rented a car from Hertz at Cape Canaveral and had no issues. The van was right there to pick us up. We were on the NCL Gem and the NCL Dawn so they were waiting for passengers to show up.
According to the shuttle driver Hertz is the closest rental car agency to the port. We just rented the car for the day to go to Typhoon Lagoon one year and Kennedy Space Center another year.