You wouldn't replace it with "romex," you'd use "boat cable" which is marine-grade stranded wire. And probably terminated with crimped-on ferrules to attach to the outlet. But yeah, that would probably be OK as long as there aren't any big loads on it. As a general rule, I only use 12-gauge wire for a string of outlets. Because you never know what someone might decide to plug in to there, some day*. Maybe 14 for a single outlet with a 15-amp breaker.
*A couple of times, when I rented out my basement on AirBnB, I found that people had brought a whole kitchen-worth of small appliances and tried to run them all on the bedroom circuit. Plus a space heater!