That's not occurring since Mihawk declared Shanks unworthy of a match due the loss of his limb so there's no reason for now to believe the two of them would clash.
Yes, he lost an arm but didn't Zoro lose his eye in the 2-year training too? That has never been shown to be a handicap for him so why Shanks? Zoro has only gotten several times stronger. Never had any problem with his right-hand side vision, did he?
We know for a fact that Shanks wasn't a yonko back we used to duel with Mihawk and only became one 6 years ago. How does Mihawk know that Shanks hasn't gotten any stronger from back then even after losing his hand?
Sure, Mihawk can definitely be stronger than Shanks but he has no reason to be so sure about it. The arm thing is such a lame reason. Was one-armed Shanks less worthy for the duel than Pre-Timeskip Zoro? Bullshit. And to tell you for a fact, I do believe Mihawk does have a slight edge over Shanks (though, I've reserved my real judgement for when we see them both in action) but the reason he gives to not duel is petty.