thats pushing it a bit but I do believe aokiji will win.Come a person who even fought whitebeard and didnt lost can easily beat mihawk. He can freeze mihawk easily.
I'm sorry, the only person as of now, who's haki is comparable, if not better than Shanks', is Rayleigh.Mihawk will take it high-extrem difficulty i believe. He will slice everything up exactly like how he cut thru a mountain size ice like it was nothing. His haki must be great enough to rival even a yonkou like Shanks when he had both his arms
And your proof is? Shanks is a swordman who used to battle Mihawk in the past, battles that were said to shake the entire grand line. If both are swordsmen, the difference can only be made in their skills and haki. When Mihawk encountered Shanks to talk him about Luffy's evolution, he talked about an unsettled battles in the past, so they were around the same level before Shanks lost his arm. Probably it's even after that incident, that Mihawk was re-knowned as the WSSI'm sorry, the only person as of now, who's haki is comparable, if not better than Shanks', is Rayleigh.