I don't think of it as contrived at all...instead, I see it as a refreshing change from
Kate. To me,
Kate is a bit staid and grandmother-ish (just a bit) but
Cate sounds more modern and creative. I would also assume that the Catherine/Katherine difference would determine the nickname. One other thing - for some reason I associate
Cate with the UK, Australia, and New Zealand. Don't know why.