OP have you discussed with him how would react if the cat was injured or killed by his nail 'defences'? So, there's a horribly maimed, bleeding, yowling cat in your garden, which has perhaps had its stomach ripped open by his nails... now what?
Does he 'put it out of its misery' himself, if so how? Does he rush it to a vet, if so which vet and then what? Does he run over to the NDN in a panic, either with or without the cat, claiming he 'found it' like this? Or admit to them what he's done? Or would he watch it die a slow and agonising death, then display the body on a post and celebrate his 'victory'?
I'm just not sure he's really thought this through. But, it might be a revealing conversation to have.
The thing is, there's a world of difference between a deterrent and a vicious defensive weapon. It's one thing (though an interesting thing in itself) to get obsessed with defending your garden from the cat, using harmless deterents. Another again to fantasise about killing next door's cat. It is quite another to take physical steps towards achieving this. It definitely reveals something very wrong about him. I think you do need to find out whether that is a mental health issue or a personality trait. How you respond would be different but, either way, you need to respond to something which is not only about cat poo.
On those pesky squirrels juneau, (they really won't go away, will they!), I outlined current conservation action upthread. The point is that this is focused around the remaining red squirrel populations. It is part of red squirrel conservation. There is no programme to eliminate grey squirrels from the UK but I do see you acknowledged that. What follows from that, is that somebody killing squirrels in say Birmingham, or Surrey, is acting in a way that has nothing to do with red squirrel conservation, so the non-native status of the grey squirrels, in those places, is of no relevance. They are simply killing squirrels because they want to. Rabbits, moles, pigeons and other animals (some native, some not) are likewise killed by gardeners who find them annoying. Sometimes humanely, sometimes not. Which brings us back to the point of the discussion.