'Wren' short for Katherine

JK
Katherine (& Kathryn) is a family name for both my husband and I. If we have a girl, we intend to name her Katherine. But as you can imagine we have lots (too many) Kats, Katie's, Kate's and more. 
Secondly my husband has always called me Jenny Wren, like the bird. 
We'd like to use Wren (at least phonetically ) as a nick name for Katherine. 
I'd love suggestions on how you would do the spelling for Katherine & wren as the nickname??