AV-8/Sea Harrier: 1 engine.
A-7 Corsair: 1 engine.
F-8 Crusader: 1 engine.
A-4 Skyhawk: 1 engine.
F11F Tiger: 1 engine.
FJ Fury (navalized F-86): 1 engine.
F9F Panther/Cougar: 1 engine.
Shall I continue? There are more jets on that list just for the USN, much less other nations.
Single-engine has never been, and is not now, a disqualifier for naval aircraft.