I like building Kat AP so getting kills and stacking my Soulstealer is important. I try and play agressive early especially but most of kills if I had to guess at it come from Lotus. You want to pop it when you know they have used their disable/silence. Take advantage of Voracity and be picking out your next target before you drop the first one. I generally just play hard and use my abilities to best benefit my team. Stats and kills in general can be a good ballpark but they don't tell the whole story.

If you are winning games thats all the matters really. If being an assist champ fits your playstyle then do it up, no shame.

while getting kills on kat looks important its actually not necessary at all, her passive giving you 50 gold and refreshing your spells on assist aswell as kills means you loose very little gold for assisting and help whoever got the last hit greatly given your not a hard carry your team wins there. this way you can spam your spells to gain stacks on snowball items(leviathan is amazing on her) and still get plently to gold.

as for getting the kill you just need to time shunpo well or the killing blow, but i dont recommend KS's someone elses hard work unless they are likely to fail to get the kill. if you treat kat like a support mage then you will see how she plays where assist are better than kills.