I like
Christabel and I like
Kitty, but I have great difficulty in connecting one with the other.
I'd use
Kitty as a nn for
Katharine. I wouldn't use
Christabel at all, as it might (mis)lead people to think that my family and I are religious. For the same reason, I wouldn't use
Christiana, even though it was the name of two of my great-great grandmothers.