That's a good point Ken.Some thoughts:
1. I assume the run time is relative short compared to the non-run time. With that circuit the 9V battery is driving the relay during the non-run time. Swapping the pot and the LDR will have it driving the relay during the shorter non-run time.
<snip>Ken
Some folks have a thing for the mains. They don't want to mess with them.As a repairman, I open these things up in a matter of seconds and I am amazed at the amount of work you are willing to do to avoid putting a pair of alligator clips on the compressor terminals.
It is rare that I question the OP's intent, but this one is so different from my point of view that it has provoked me out of my silence.