There are a million problems with the idea that Shanks is definitively above Mihawk. But I think one of the most glaring ones that people don't speak about enough, is what to do when Zoro actually defeats Mihawk.
Zoro believes that, in order to become the World's Strongest Swordsman, he has to defeat Mihawk in a 1v1. He will be using haki, and he will definitely be using ACoC. This panel pretty much proves it:
So, if Zoro will receive his WSS title by being capable of defeating the current WSS in 1v1 combat, why doesn't the same apply to Mihawk vs. Shanks? Do we expect Mihawk's swordsmanship to still be considered better than Zoro's even after Zoro defeats him?