On our
Disney Cruise to the Western Carribean we did our own tour in Grand Cayman. We hired a taxi to take us to the Turtle Farm, Governor's Mansion, Hell, and 7 Mile Beach. It was significantly cheaper than the same tour offered through Disney with virtually the same experience(s).
Keep in mind, if your excursion is booked through Disney and the there is a delay in getting you back to the ship (or to water taxis) Disney will wait for you. If you're on a non-Disney booked excursion and there is a delay, the ship will not wait for you and you are responsible for getting you and your party to the next port to board the ship.
So there's a good side/bad side to doing your own excursion. If you do your own, schedule it early enough in the day that you know you will be back on board before the ship leaves port!