I believe in this case a pos/neg fence system, if the wires were close together, would work, right? They wouldn’t have to be touching actual ground. They could be on top of the board, touch both wires, and zap! But from what I see those systems aren’t made for small critters.
Yes, that kind of system is made for larger animals.
I don't know if Premier 1 makes a pos/neg netting. I've never looked into it.