Katarina is a well known champion for her multi-kill potential (and also one of my personal favourites) so you shouldn't stay away from teamfights. It's possible that you get lots of kills and you can easily make your escape with Shunpo if the opponents start focusing you.

Farming is very important when playing as Kata. So try to max sinister steel as soon as possible. The use of this ability will allow you to take out dozens of minions at the same time!