The electrical current in Grand Cayman is 110 V, 60 Hz AC; i.e. same as the States and Canada. Two-pronged, flat plugs are in use.
European visitors will need to bring a hammer to force their rounded plugs into position. Travellers from the UK (3-pronged plugs) will need a drill too. Your hosts may be keener to see you again if you purchase an adapter for your appliances.