Transistor is always in saturated mode
Assuming that the wires you mention originally connected to the forward and reverse switches on the remote control, the safe way to have the Pi control two relays, with the relay contacts connected where the switch contacts were connected (or in parallel with the switch contacts).  The relays will provide electrical isolation between the Pi and the unknown circuit in the remote control, and won't care about polarity.

Any solid-state solution would require some knowledge of the controlled circuit to be sure of correct operation.