Zoro still regards Mihawk as the obstacle to surpass as shown by his fight with King.
Because as things stand right now, Mihawk is his obstacle to surpass.
But if someone kills Mihawk, Zoro’s aim shifts. There’s a new WSS, Zoro still wants to be the WSS, and now there‘s the added incentive of Zoro getting revenge against the person who robbed him of his fight and murdered the guy he spent two years training with.
Zoro can fight Mihawk after the Final War.
No he can’t, because the final war is exactly as it says on the tin- The Final War.
It’s where everyone’s final fight will be. It’s where the most important fight in the series will be, Luffy vs the final villain. Oda is not going to draw another fight after it, and the readers have no reason to care much about another fight after it, because the stakes will be the highest they can possible be.
Zoro is not the main character. So he’s not getting the final fight. Luffy will. And I have zero reason to think that Oda, who’s pretty much said time and again that he wants to finish One Piece and thinks that fights delay that too much, is going to finish his great final arc, worldwide war… and then draw another fight between Zoro vs Mihawk right after it. That’s simply not something he’s going to do.
Several Strawhats wouldn't fulfill their dreams until after Luffy has become the Pirate King:
None of these Strawhats have dreams that are specifically about fights, which Zoro has. That’s what ties his deadline to achieving his dream to before the final war ends, because the final war is the unquestioable, best and last, place to have a fight with the stakes the highest they can possibly be.
Nami and Franky’s dreams can be shown in a montage that shows the crew stuck together after the war, had adventures, and then ends the series on a nice note. It’s a nice little capstone to the series, good epilogue material that can provide the usual “the world recovers” timeskip epilogue that most series get.
It is because Zoro holds Luffy's dream in higher regard than his own that he would ensure the fulfillment of Luffy's before going back to fulfill his personal dream.
Or he’ll just do it on the path to making Luffy’s ultimate dream comes true, which makes much sense.