The man is portrayed above Shanks' level by a decent margin and Yonko are not irrelevant in Wano so that's far from constituting reality.
But Mihawk is not a Yonko, and for sure Kaido and Mihawk never had a duel.
Also even if Wano is the land of samurai, Wano Arc's plot is not about who's the strongest swordsman is.
So story-wise Mihawk is irrelevant to the current Arc's plot.
That's why Ryuma, Wano's hero, was the one who was hyped when Onimaru and Zoro were having a conversation about the black blade.
To me If Oda choses to hype Mihawk there and then directly, it would lessen the hype of the characters related to Wano (Ryuma and Oden).