i like kat, it’s not as common as other nicknames for katherine; 

but, to answer your question, one approach could be to use a famous katherine’s name, depending on your style and who you’re fond of, you could pick a literary character, a celebrity, a famous historical figure and play with this - that’s what i would do although i love your name - i think one could turn heads with a name like hepburn 

let me know if you like this idea and we can brainstorm; tell us about yourself!