I've only played as the old kat vs fizz once, but I suppose I have an idea:
When she shunpo's to ult, you could use your E to not take any damage from it. Since the duration is even less now, you'll be able to stay up and not take as much damage from the ult. You're both melee last hitters with situational jumping gap closers, although kat sort of has more burst than you. If you wanna engage, do it after she burns her skills on creeps, and the like (try not to stay in longer than her new W's cooldown, I suppose).