What about
Christina - Chris, Chrissie, Christie, Tina.
Alexandra - Alex, Alexa, Andy, Sandra, Sandy (ok, the last two are a little stretch but it's accent depending)
Josephine - Jo, Josie, Sephy,

I think Catherine is fine, yes the Gaelic Caitlin is a form of Catherine but the two names are so distinct now, especially with Caitlin's numerous variant spellings, of which yours is one, so I don't think it's a problem at all. As long as you don't have her go by the Kait/Cait spelling I think you're good to go.