i fished exuma last year with 2 guides and 6 days of DIY, the guides were very gracious and the island is SO massive that you can find flats in almost any area without getting in their way.
i have no idea what the other poster was talking about
you really need a satellite map and a jeep, follow the old dirt roads to the various flats. the entire west side of the island is loaded with them from the south to mid island.
the north end also has many accessible flats with no signs of any other anglers at any time
if you go, you may want to bring an inflatable tube, (its hard to find a kayak for rent) inflate, get across to the flats and tie it off ..
if you are going the week of Apr 9th to 20th i will be glad to show you some spots that are barely fished