Just take it apart, I'm pretty sure it's just a "potentiometer"
(variable resistor) so it would only have 3 leads, one from the external
wire to the pot., one from the pot to the motor, and one from the other
external wire to the other lead of the motor.

Cut things off, plug the external leads directly to the motor.



Unfortuantely it doesn't seem that simple. The speed control has what
looks like a some kind of semiconductor/IC (3 leads), a diode, and
maybe a fixed resistor in addition to the slide pot. I don't know if
they're doing pulse width modulation or what.