I’m sure you can return the cat to the shelter, but there’s a good chance it will get put to sleep there.
Two steps I think you try (simultaneously, since it sounds like you don’t have much time) before doing anything that drastic:
1) Buy some Feliway spray. If you r local pet store doesn’t have it, you can order it online, or your vet probably sells it too. It’s a pheromone that has a calming effect on cats, and often helps reduce or prevent marking behavior.
1) Check with a vet about psychoactive medications. I once had a cat with a MAJOR peeing in around the house problem (did it for attention — peed on the cable box on top of TV when people were watching TV, peed on the sugar bowl on the kitchen table when people were in the kitchen, peed on the coffee maker on the kitchen counter when coffee was being made, and would leave a big puddle outside bedroom doors that were shut to keep the pee-monster out). Just one little amitriptyline pill daily put a stop to this. Poor little fella was just feeling anxious about life in general, and peeing was the symptom. Also, if at all possible in the neighborhood you’re moving to, install a cat door, and let the kitty come and go freely.
That is treading dangerously close to death penalty territory.
I think that sounds like what is going on here. We have sold our house and there is some major construction going on outside. It must be making him nervous.
Good Lord! It's a wonder the poor guy didn't accidentally electrocute himself.