Stepper drivers and simple PWM drivers work differently.
Stepper drivers typically have a H-bridge to drive the motor coils. This allows current to flow in either direction through its coil.
The PWM driver looks like some sort of astable chip, whose output is adjustable by the pot, and there's another chip that could be a MOSFET in SOIC package.
I would say you can use the PWM driver board and hook it straight up without additional inductance, but your input voltage must be the same as the voltage to drive your LED strip, otherwise if you wind the wick up too far you could blow your string.