I removed the volume knob/power switch from the CB and tested those controls with the HHCH, success!

The power switch uses a 12v SPST relay to turn on the CB. One leg of the coil is always hot, the other is provided with ground by the power switch on the HHCH.

The volume was as simple as replacing one with the other. The CB had a 10K pot for volume, while the HHCH has a 20K. I removed the pot from the radio, and via the breadboard connected the volume knob on the HHCH. I added a 22Kohm resistor in parallel so that the maximum resistance would be approximately 10Kohm, although the difference in lower volumes with and without the resistor is negligible.

Next up to figure out will be squelch, it's going to take a bit of work as it's going to be a digital pot driven by the Arduino. I've not worked with digital pots before.