Sorry but the only reason Zoro would have to cut Kaido is to mimic Oden. Guess what? Scabbards already cut Kaido. Multiple times. The significance of that is gone, Zoro has no beef with Kaido.
Kaidou: "I would have been fine with letting myself killed.
There will never be any samurai as strong as Oden!
Your power isn't enough to kill me!!"
The wound caused by the Red Scabbards with the "Togen Totsuka" makes Kaidou bleed, but isn't enough to reopen the old wound Oden caused him.