Looking at the picture the OP supplied in post #6, I would have said that the hand held device is part of an electronic motor controller circuit and not simply a variable resistor in series with the motor.
It all looks dimensioned for much lower power than that, also with fine connectors etc. Also, the slider potentiometer has B10K printed on it which could imply a 10K ohm resistor. Maybe the OP can measure the resistance across the potentiometer while the switch that is also visible there has something preventing the contacts touching each other, and the plug removed.
When I used to play with these things (many, many years ago) the hand held controllers were then indeed low resistance, air cooled wire wound resistors, but I guess the technology has moved on since then.
That does not, however, necessarily imply that the selected digital potentiometer is a viable replacement, for the reasons already mentioned.