Best options for ice/trash in the northern half of the Exumas are Highbourne Cay, Compass Cay, and then Staniel Cay. In the Land & Sea Park you are on your own. Have never seen a vendor come around anywhere.

We have a crew member that is relentless about replenishing/rotating beverages in the fridge/freezer. Gets easier as space frees up during the trip. Keep a bag of ice in the freezer for cocktails. Can also ask for or rent a 2nd cooler from the charter company.