I’d laugh at how hilarious it would be.
It’s something that I have considered though. It would be an interesting twist if Shanks had beat Mihawk on the condition that Mihawk join his crew, but Shanks discouraged it from being known and encouraged Mihawk joining the Shichibukai so that he could have a window into the WG the same way Doflamingo used Vergo with the marines.
It could explain why the first thing Mihawk did after meeting Luffy was go meet up with Shanks, and why Mihawk bailed in Marineford (unless he’s not affiliated and just didn’t want to get his ass whipped).
It would be a cool twist, and would make a bunch of people mad.