no mihawk is not confirmed to be stronger than shanks, people need to realize there's a difference between strongest swordsmen, strongest pirate, strongest marine, and strongest person.
Strongest swordsman doesn't put you above anyother swordsman, it just means that strongest swordsman is better in sword art than any other man in the world. That doesn't mean that you are better than him in devil fruit usage, haki, stamina, etc..
When it comes to Shanks and Mihawk it's pretty deep.
- Mihawk is stated to be strongest swordsman, Shanks is swordsman. Shanks doesn't have devil fruit (as long as we know, 10 years ago he could swim), he showed great haki, Mihawk's haki is unknown. Shanks' primary weapon is sword art (every time he was shown fighting he was with sword), so Mihawk is better than Shanks in his primary weapon. So how much haki can close a gap between their difference and how strong is Mihawk's haki is?
Also, in the past Mihawk wanted to fight Shanks (assumption - Shanks
was one of the best swordsmans around and by defeating him, Mihawk would gain title strongest swordsman). We know somehow Mihawk gained that title (assumption - he beat Shanks), we know Shanks was hidding in the weakest see for year, why? (assumption - he was ashemed after his lost).
It's a lot of speculation considering we need to see their past, but atm most likely assumption is that Mihawk is/was stronger.
Shanks could get stronger in last 10 years, but I doubt Mihawk was just sitting around while Shanks trained, and he got handicap by loosing one arm.
Garp said that Yonkos are strongest pirates, but even then not all translations refers to them as strongest pirates, some of them refer to them as "Strongest pirates in the New World", Mihawk lives in paradaise, so in that case he is excluded.