In the USCG, the hoist operator is the Flight Mechanic, who will normally be either a AET or an AMT (Avionics Electrical Technician or Aviation Maintenance Technician).
The Rescue Swimmer will be an AST (Aviation Survival Technician). While some ASTs are qualified as Flight Mechanics, they are fairly rare, and in practice don't perform the duty, because they're usually hanging on the hook or administering medical treatment when aboard the aircraft.