https://mfcoutdoorstores.com

If you pop in and see Clive, he will sort you out with something.
He will also if you pop back to collect, set up and zero your rifle for you.

Last time popped in they had several cheaper springers that would be ample for your needs, or a CO2 - both new and second hand.

Smooth cheap peanut butter and cheap chocolate spread will be your friend - keeping them still long enough to shoot.
If you are seeing them daytime - that is a bad bad sign.
You might need a cheap torch on your scope - ask on here for solutions

I also do not think relocating grey squirrels or rats is legal as they are absolute pests