Last year, my wife and I did just what you are looking for. We did Stingray city early, came back to the docks and caught a taxi tour. They try to get six people in a taxi, small van, and have a set tour but will sway from that if the passengers agree. They gave us a nice overview of the history and politics of the island. We went to hell, the rum factory and the turtle farm for $15 per person and had a blast. It ended up a little rushed at the end only because two people in the taxi were on a ship that left earlier than ours. We are going back in 3 weeks and would not hessitate to do it again. It's a great choice, because you can do it spru of the moment.
Happy cruising