Canonically, Mihawk stopped fighting Shanks before he became a Yonko.
Canonically, Mihawk remained stagnant and waits for somebody stronger than Shanks was back then to defeat him. While Shanks got stronger sailing on the seas.
You want to bring up canon like Oda didnt just finish wrapping up the timeline of these events. Shanks was releative to his Yonko peers through his Haki alone. The same Yonko Mihawk isn't stronger than.