Their height information comes from the same Data books that directly state that Mihawk is waiting for somebody to surpass Shanks and give him a worthwhile fight. So if you want to do height scaling via relying on Data books? Cool, the same Data books tell you Mihawk is stronger than Shanks regardless of the supposed "1 cm" difference saying the opposite.
Oh, and btw for anybody that does LEGIT height scale them based on the 1cm difference and does not just troll for the lulz? You are legit the worst powerscalers I have ever seen. Motherfuckers mememing about blue Haki Arlong are intellectual heavyweights compared to you bozzos.