My wee yorkie was neutered when he was a year (we've only had him about 15 weeks) He never ever pees in the house if he is bursting he cries to go out but every now and again he dribbles what I think is pee on the couch when he's lying down, sometimes I think it's maybe him licking himself as it's not that wet and other times it's quite wet but not a full pee and it doesn't stink like pee either!
Our female lab did this all her life. She was on some medication to prevent it - urilyn syrup or something - not entirely sure as she was our "family" dog and mum dealt with the vet stuff! Not sure if the same thing could affect a male westie but worth checking, I guess?
We had this with out dog. The first drug they have us was propalin syrup and didn't warn us that one of the side effects could be aggression. Our gorgeous playful spaniel has never been the same since. After another £1500 on training (and 2 years later), she can finally be near another dog without attacking it, though clearly doesn't like it.
In terms of the urinary incontinence, that's cost us about £5k and after numerous tests and an operation (which didn't work), she's finally under control taking two tablets a day for the rest of her life (incurin). They didn't give us these to start with as they are the more expensive option; but I wish they'd given us the choice!
(Sorry, really hope your experience is different. I'm still quite bitter about the whole thing!)