I don't suppose the back side of the wall could be opened?

There is one trick you might be able to use. If the baseboard is at least 2-1/2 inches tall, you can run the wire behind the baseboard by cutting a slot in the sheetrock and covering it up when you replace the baseboard. You should put something in front of the wire to protect from nails though. Still a bit of work but much less effort and not as messy as tearing down the wall.

I could draw a diagram, but I’ll keep it simple and say “no”. The lights are in the ceiling and I have no idea how the wires run, whether through the wall or ceiling or both. One wall backs onto the finished garage, the other route would be the finished ceiling which doubles as the kitchen floor. The switch location is on the other side of the hallway. I got the wireless kit and will report on the result.