No one said Roger was World's Greatest Swordsman.
So by default, mihawk should be > Roger too.
But in truth, that title is meaningless when it comes to top tiers.
Let alone top-tiers, we didn't even see a high-tier wanting to be the world's greatest swordsman, if no one cares that, how can that be better than top-tiers when Shanks is a top-tier himself.
Either way, mihawk is irrelevant to this story, I've been telling this long time ago, before they removed mihawk's title, mihawk's fans were saying mihawk will fight alongside with world government in the final war, so now they removed mihawk's title, that option is no longer avalaible. But mihawk fans are still dreaming on mihawk will be relevant to the main story somehow.
And there are even people talking about shonen story logic
How can a guy like mihawk, who is irrelevent to the main story, showing up as more powerful than even Shanks, Luffy's last or second last opponent before becoming the Pirate King... I guess that make sense for them in terms of story telling.