Yes he fights with a sword and haki. The point being made is that Haki and Swordsmanship are not directly related. I said Zoro will surpass Mihawk in both, and I meant it, because that is likely true.
However, I do not agree that Haki proficiency = swordsmanship proficiency, because Haki is not exclusive to swordsmanship. You can have stronger Haki (i.e. Roger) and be a worse swordsman than Mihawk, that doesn't mean you will lose in a fight with Mihawk. It also doesn't mean you will win in a fight with Mihawk.
Literally Luffy vs Katakuri. But of course, you don't get this, even while Shanks and Mihawk have never bested each other. Swordmanship does not have this exclusive hold on haki output. I'm sorry, I don't agree with you