Of course the current is "tiny"
You are driving the pot with a 3 volt supply into a 100k pot so the supply current will be 30microamps
The control box must have some form of identification on it such as manufacturer name, model number etc
I surmise, if you go for a PWM (with RC filter), you can ignore the control supply of 3 volts and simply connect the filter output voltage between the control ground and control input - after having ensured it can never exceed the 3volt signal maximum. But information as requested previously should indicate the input limitations.