The point is:
Mihawk surpassing Shanks in swordsmaship/skill with the sword doesn't mean he's overall stronger than Red Hair since swordsmaship Is not even the thing most hyped or emphasized about Shanks, but his CoC, even though Shanks Is still ricognized as a formidable and top class level swordsman, his swordsmaship Is the #2 thing about him, while Haki being the #1 emphasized about him as seen several times, so Mihawk surpasses him in his 2nd best thing but not on the thing most emphasized and hyped about him.
That's simple and easy logic guys, please get It.
It was never stated that Mihawk surpasses Shanks in his forte, the thing most emphasized about It by other characters when he showed up on screen, by Jozu, Greenbull and his crew, his insane haki.