??.. Great Pirates exist without the One Piece.. Mihawk is washing his neck and waiting for Shiryu..
Mihawk's hype will be to defeat S-Hawk, then he will be Shiryu's hype tool.. Blackbeard - Shanks, Shiryu - Mihawk..
You still don't understand the manga.
Mihawk was already a renown swordsman before the great pirate age. His WSS title is not a title limited to the just pirates. He doesn't need One Piece to exist.
Mihawk received hype during Marineford when the manga hyped his strength beyond the combined power of 3 admirals.
You still think those pirate titles and positions mean something to Mihawk? He could have been a Yonko but he chose not to because he doesn't care for it.
S-Hawk and Shiryu will be stepping stones to help Zoro prepare to face Mihawk. The same as all of his opponents. Including BM and Kaido. They will used to hype us Zoro's CoA haki, AP, and defensive power.