Both Dream Yacht Charters and Cruise Abaco have monohulls available for charter in the Abacos; Navtours has a few monohulls for the Exumas.

While we had little trouble with our own monohull (draft approx. 5' with a wing keel) -- only hit bottom once in the Abacos -- why not give a cat a try? Unless cost is an object, cats are ideal for the skinny waters of the Bahamas, letting you tuck in closer to shore if you choose. Of course, cats involve some compromises in sailing performance, but in the Exumas you won't be doing all that much sailing; in the Abacos, you do a lot of beam reaching in the prevailing winds, so a cat is fine for that.