I agree, use the airlines, either Tropic or Maya.
Try to get off the ship on an early tender, they usually reserve the early tenders for the organised tours, but the earlier you get to the tourism village the more time you will have on Ambergris Caye. Once you get to the cruise ship tourism village, you will need to exit through the nearest terminal out to the road, this is hardest part trying to get a taxi to the municipal airport as all the taxi drivers will be looking for a tour that makes them some money!!!!!
If you struggle outside the tourism village for a taxi, walk towards town and the water taxi terminals and you will get a taxi to the municipal airport.
Remember, there may be a time difference in Belize and the ship's time, please check. The flights leave the municipal airport in Belize City to San Pedro 30 minutes past the hour and return on the hour.