Staple through a small electrical wire, will it still work correctly?
Wrong kind of staples. Eventually they might all abrade the cable, whether or not you stapled right through it and present a fire hazard. Replacing the cable would be best. Inspecting the damage would be good, but then you'd have a splice to deal with or have to re-insulate, both having to be waterproof. Damaged insulation can be fixed, but we don't know how bad the wire got nicked (also a fire hazard).

Plastic Insulated Cable Staples: (Ideal)