No marine experience, but as a home inspector I sometimes run into electric tankless heaters and find they rarely perform adequately for bathing purposes.
If you are planning to use it for low-demand use (washing hands, dishes, etc.), then a 110V on-demand heater might suffice. For showering, I would be surprised if it could supply enough volume to be satisfactory. In any case, it would take a very hefty extension cord since the longer the run, the bigger the conductors must be. Keep in mind that the temperature of the fresh water supply will have a considerable impact on the performance of the unit.
This is likely the reason that most marine water heaters are "recovery" type where water is kept hot in quantity (5 gallons or more), used, then allowed to recover.