The secret about what happened in the void century is in a laugh tale, it will even be the trigger for the rebellion against the WG, so Luffy will be the Pirate King before the final war.
On the other hand, Mihawk is not an agent in these events, he has no interest in any of it, much less would he side with WG to fight Zoro. Also, he is the strongest enemy Zoro will face, it doesn't make sense for Zoro to have other fights after this one as they won't pose any difficulty, unless he has to fight and defeat two admirals. Finally, he and Mihawk don't need another justification to fight, both want the fight, Zoro just needs to reach that capacity and when that happens, Mihawk will accept another challenge.