OK, I watched the video. They are using some loose terminology there. When they say power they mean 120VAC. They don't really mean there is absolutely *no* power on those wires, its just a control signal not supply power for the fan. So the red wires do not carry 120VAC. They must carry a small current at some (probably DC) voltage supplied by the internal components in the fan. The switch makes or breaks the circuit and the fan's internal components see that and deal with setting the fan speed. So, you definitely don't need a relay that's rated for 120VAC. But I still think you need some form of relay to do this job and an SSR will likely be more reliable in a marine environment. This page lists several alternatives. I would think you'd want to put a meter on the two red wires and see exactly what voltage and current it had so you pick the right relay.
http://www.jameco.com/1/1/730-kf0604d-dc-dc-solid-state-relay-control-voltage-3-32vdc.html