Yeah, the single wire alternator doesn't need an external regulator, it has a built in internal regulator. Simply run a charge wire from the battery terminal on the alternator to the positive terminal on the battery. (solenoid) The one-wire regulator is a self-exciting regulator, meaning that it has sensing ciruitry for alternator rotation. As the alternator starts to spin, this circuitry connects the internal voltage regulator to the battery and turns the alternator on. When the alternator comes to a complete stop, this same circuitry turns the alternator off.
You can either use some cable ties to get those extra wires out of the way, or remove them and the exterior regulator altogether.