Think of it like this:
Mihawk's title in Japanese is written exactly the same as Whitebeard's title and Kaido's title. The most logical interpretation of both Whitebeard's and Kaido's titles is that they are stronger, as in more powerful, than anyone who falls under the same category.
Anything that is considered a "creature" should be, by the title, weaker than Kaido. The same goes for Whitebeard.
Why is Mihawk's title treated differently, when it is written in the exact same way as the other two?
Realistically, the only logical way to argue in favor of Shanks is by claiming that he's simply not a swordsman. He can't be stronger than Mihawk and be a swordsman. It's one or the other. The only issue is that trying to argue that Shanks is not a swordsman is a very steep hill, considering it's not something that's ever been suggested in the manga.
Admittedly, Shanks' portrayal and place in the story is confusing. He seems to be much "bigger" than Mihawk in the One Piece world in terms of influence, and he's also heavily tied to the main character. That's why it is definitely possible/probable that Shanks has something, I don't know what, that Mihawk doesn't have in order to match up to him in some way. I'm pretty sure Oda even said it's very difficult to rank/compare two top tiers unless they have a full-fledged 1v1 anyway.
I think Mihawk >= Shanks is a pretty safe bet, with some margin for error.