No, removing the partial refund on W/nerfing E isn't going to impact tank Fizz.
AD on-hit tank/bruiser Fizz doesn't have a hard time CSing regardless because his matchups are almost all melee outside of the occasional Quinn or Vayne or Teemo or Jayce because this happens in toplane.
AP Fizz is against an equal diversity of melee and ranged matchups in mid. Some sort of CSing mechanism is necessary whether you like it or not because of the frequent ranged matchups. No, it does not automatically make him good at CSing enough to overcome the difference. Ranged matchups still abuse the hell out of him prior to level 6 and can shift gears and play defensively post-6 and push when he's roaming or roam elsewhere.
There's a difference between being simply weak in laning and not being able to CS reliably at all because literally every single time you even move slightly towards a minion, the ranged can poke you with either autos or abilities and bully you out of your health. Sure, you hit your level 6 spike eventually. Congratulations, you will probably have either died a few times by that point or taken even larger CS losses to avoid dying because you have to dance around behind your own tower with 10-20% health to avoid dying from ranged poke past tower while trying to get what CS you can. You will be behind on both experience and gold to an extreme extent making you a lot weaker even by the time you should be able to do alright.
It's the reason old AP Fizz had damage amp. It's the reason new Fizz has partial refund (no it doesn't completely reset it, it's still a 1 second cooldown nor does it ever fully refund the mana). It's the reason Zed can sacrifice W+Q+E to farm at the cost of losing all his abilities and his one mobility tool pre-6. It's the reason Talon can farm with W in return for a high mana cost and losing half or more of his damage pre-6. It's the reason Akali can use her mark procs and Shroud to farm somewhat safer. Same for any other.
They are still weak and get bullied pre-6, but the difference is that they can actually still CS somewhat despite the bullying. They're still going to be bullied and hurt quite a bit and have less CS than any competent ranged laner. That's the point. They are supposed to be weak, not made completely useless and then kept useless because they are too far behind by their spike.
Top Fizz doesn't give a shit about E. If you're a tanky on-hit duelist, a survival tool meant for squishies isn't really that helpful. You'll live through almost all of it regardless. W is the biggest and one of the only reasons tank Fizz is even possible.
Mid Fizz needs the E more than just about any other ability he has. It is literally core to his survival chances and playstyle. You might hate it, but you cannot validly deny it is balanced/balanced around AP Fizz. It hasn't been exempt from nerfs in the past either for that very reason (to manage its state of balance).
If you want nerfs to tank Fizz, suggest things that would actually make some damn bit of sense. Not things that have next to no fucking impact on tank Fizz, which is the only broken form of Fizz, not AP Fizz, and nerf only AP Fizz.