Non-orthogonal multiple access (NOMA) is a promising technology to improve spectrum utilization effectively for underwater optical wireless communications (UOWC). To exploit the benefits of NOMA in a turbulent environment, cooperative transmission has been introduced in the NOMA–UOWC network. The existing studies on NOMA suggest that relay selection and power optimization are the main factors affecting system performance. In this paper, a general NOMA node pairing method and two power optimization schemes for NOMA–UOWC are proposed, and both schemes are proven to be strictly quasi-convex. The two optimization schemes are solved by the BFGS algorithm and the particle swarm algorithm, respectively. The effectiveness of the proposed schemes are evaluated by our simulations, and the main factors affecting the relay-aided NOMA performance are derived.