One Piece is in 760s chapter but it's still early to say who out of these two is better in which category. We can only say that Mihawk is better than Shanks when it comes to swordsmanship. I would say that they are pretty equal and if I had really to chose one I would say Mihawk instead of Shanks, but as I said it's really early to say who out of these two are stronger.Yes, they don't fall under the category of swordsmanship, but a user of such is still considered a swordsman overall. Shanks can be faster than Mihawk, or physically stronger, or have stronger Haki, that's all fine and dandy, but all that means is Mihawk is strong enough to not be defeated because of that; Mihawk has some trait that puts him above all swordsmen. Maybe his stamina is too great for swordsmen who are physically stronger than him. Maybe his skill with a sword is too great for swordsmen who are faster than him. Maybe his attacks are too overwhelmingly powerful for swordsmen with better Haki.
That makes both of them swordsman, but that makes Mihawk > Shanks in swordsmanship, who is overall stronger is just matter of opinion.
As I said by the end of series, Zoro will be Greatest swordsman, but it's pretty unlikely that he will be stronger than Law, who is also swordsman, he will just be better than him when it comes to swordsmanship.
As I said to Riker Slade above, it's early to say who is better than who in which category.Like I was saying earlier, maybe it's CoC that sets Shanks above Mihawk.