6V wiring is heavier than 12V, so if it's in decent condition there's no problem leaving the original 6V wires, no relays required although some folks like to use them for the headlights
the foot starter switch doesn't care about voltage, but to use your foot starter you need to have the correct [6V] flywheel tooth count, 139 teeth .... it may be that the solenoid starter was from a 6V car, so the flywheel might be from a 6V, but if you have the 168 tooth 12V flywheel, you could find a 12V foot starter, 55.2-60
Bill