Gonna start off by saying I don't think Zoro did a whole 2 years training with Mihawk. I remember Mihawk asking Zoro why he would train someone who wants to take his head (something along those lines) although later accepting I think he still partially refused to train him.
I think Mihawk instead took him to other swordsmen on the grand line to train/fight him (especially since we know the SH didn't visit every island in the first half of the grand line). Although I have no proof of this, it seems more plausible. I do think Mihawk taught Zoro the basics of haki as seen when he is telling Zoro about any sword becoming the black blade.
What do you guys think ?