It could be because I am studying Irish but I have never read this as cat-hair. If anything I have only read it as cath-air. But it's pronounced ka-hir. If you're worried about people mispronouncing, you could use Cahir, which is the same name. Anyways, I really like this name and I think it's really nice. However Cathair means city in Irish so the fact that this doesn't mean city surprised me.