Katarina is actually really bad on urf. She's a trap pick that looks like she'd be powerful because "omg damages", but is actually made super useless because hard cc and defensive moves are on super low cooldowns, and her passive is basically useless because resets mean practically nothing on urf.
If you want easy wins, play AP tryndamere. 1:1 AP ratio on an aoe dash with a cool down around 1 second at max level, combined with a free 3 sec cd heal that scales with AP and fury that stacks super fast, and a 20 second cd "fuck you and all your damage" spell that lasts for like 5 seconds. And a slow if the person is somehow outrunning your spin dash. Rush Luden's Echo, because in urf the most op champ is Luden's Echo, and then get a deathcap into lichbane. Proceed to win every game with no deaths and at least 20 kills and assists. You will beat ezreals, kats, nids, ziggs, leblancs, you name it because they can't poke you out before you hit 6, and they can't kill you when you hit 6.