yeto:
using "just" a PWM motor speed control that includes a potentiometer and "not" using an Arduino board?
You will need some device to detect the position of the potentiometer and then to generate the appropriate PWM signal. I can't think of a simpler way to do than with an Arduino of some sort.
I guess you could do it using a 555 timer IC but to my mind it would be a lot more trouble even if the parts are cheaper.
...R