I don’t think the Combat Side Stroke is possible with only one-arm, but it doesn’t mean it’s impossible. Impossible means you just have to do some modification of the technique to fit your physical limitations.
I think you should consider swimming one-arm freestyle. It’s my favorite drill and I always start my swim sessions with several laps of one-arm freestyle with my non-pulling arm by my side. If you have difficulty with it, try using swim fins.
Here's a video demonstration of one-arm freestyle swimming with the non-pulling arm at the side. Most other videos have the swimmer with the non-pulling arm extended.