We had a problem with a big dog leaving huge piles on our lawn a while back. I bought 2 of these and also sprinkled Jeyes fluid as recommended by some here across the end of our garden where it was entering. I’m not sure which option solved the issue, but no more faeces has appeared since.
Don’t cats tend to defaecate away from their places of eating - how about leaving food out to see if the beastie will eat with you and deposit elsewhere?
FWIW our repellers don’t seem to bother next doors dog, which would be in range in their garden.