One problem is the cable connectors.
The output connector on my Chromegatrol is a multipin connector.
I don't know what connector is on the input of that stand-alone stabilizer.

Another problem is matching correct input and output voltages. If the OP voltage of the Chromegatrol is 12 volt DC to the lamps, and the input for the standalone is 110v AC, they won't play together.
IOW do you stabilize the voltage before or after you convert 110v AC line to working voltage for the head.