I think it's possible that this fight might not be happening.
The main theory was mihawk is still shichibukai at the EoS when the SH Pirates fights the government, there Zoro was going to match with mihawk. But that is not going to happen now as the Shichibukai are no more, and the marines are chasing mihawk like they are chasing any other pirate.
I don't think mihawk is going to follow SH pirates in the new world, even if he does, that would only serve the enemies (Possibly Blackbeard or World government) of the SH pirates which is something E.Oda is not going to allow.
The best way for mihawk to fight with SH pirates is that if he joins Shanks, then when Luffy fights Shanks, Zoro can fight mihawk, and Sanji can fight Beckman.
There are only two options left; join Shanks or go after them individually. If mihawk goes after SH pirates in the new world, then that should be after Luffy finds the One Piece, otherwise as I said earlier, mihawk attacking SH Pirates would serve other factions if it happens before fighting with Blackbeard and other enemies. The best scenario, since mihawk supporters don't like him joining Shanks and accepting inferiority to Shanks, would be that after finding One Piece, there mihawk could individually follow SH pirates and he can attack Zoro or Zoro can attack him. Even then, I think that fight would be pointless, because at the EoS, after fighting Yonko crews, Zoro will improve himself a lot, and we will all know Zoro is going to win that fight, it would be a boring fight and it would be only for Zoro's personal goal, which had nothing to do with main character Luffy and other SH pirates, or ''One Piece''.
To make mihawk's existence meaningful, mihawk should join Shanks. Then either he can fight Zoro when Shanks fights Luffy, or this fight won't happen because Shanks could lose to Blackbeard, Shiryu could beat mihawk, and Aokiji could beat Beckman with extreme diff.