Mihawk doesn't specify at all. wss title is gotten by beating mihawk who is yonko lvl. To be pk, you have to surpass that. mihawk is the end goal of zoro. Yonko's are just a waypoint for luffy.
I really don't see much difference between PK and yonkou. whitebeard was hailed as the strongest when Roger was alive.
and being pk has a lot to do with crew as a whole. Not everyone had crew like rogers.
mihawk is yonkou level? he have facts from manga calling him above shanks who hold highest bounty at the moment.
If you believe a tier exist above yonkou. mihawk is already that level.