Hi !!!
My favourite short forms of the name are
Kitty,
Kay,
Kasia,
Karin and
Kaja.
If I have to choose another form I'd choose
Cate.
Katie,
Katey and
Katy are super boring and plain.
I suggest
Cate, at least
Kate (in my case after the Duchess of Cambridge) or
Kathy (after
Kathy Reichs).
Personal Name Lists
https://www.behindthename.com/pnl/125456