There are motor coach shuttles but the airport is only 5 miles from the pier. My recommendation would be grab a cab. It'll be less than the transfers and quicker.
You can take a bus from the cruise terminal to the airport and then get a car rental shuttle from the airport. This is the inexpensive way but I would also look at the car rental company websites because they may have car rental offices at or close to the cruise terminal. And remember that Honolulu has one of the very best public transportation systems (buses) in the USA. And bus service is especially good between the airport, cruise terminal, Wakikki, and Pearl Harbor.