Mihawk hasn't even tested clashing with Whitebeard, how can you be so sure he would do worse than Shanks? Not that even if he did it says anything about Shanks vs Mihawk, it's a totally different matchup.
Shanks might be stronger, but clearly in their duels they were equal and that was before Shanks lost his arm.
I have a hard time believing Shanks fought Mihawk with just a one hander. That would make him better wouldn't it?
Two-hander vs two-hander would be a fair fight. I can see Shanks was able to keep up with Mihawk because of being stronger/having better haki, so what would he do now that he has a two-hander handicap?
Fight the world's strongest swordsman with a one-hander? Anyways if Shanks was in fact able to duel Mihawk with one hand Mihawk would not deserve his title. Well, maybe he was just using that dagger
Anyways for it to make sense with Mihawk's title and the fact they were equal before, Mihawk is at least slightly > Shanks if they were to duel again.