I've obviously read your post and the logic doesnt fail. You brought up a bunch of technicalities that implies even Zoro isn't a pure swordsman and doesnt count.
I mean, here we have a moment, this chapter and plain as day where Kaido recalls the men who have hurt him. Every single one of them is a blade user and yet Mihawk isn't there.
You can take the argument 2 ways, either these men just happen to use swords like generic pirates, aside from Whitebeard (i.e. they are MORE than their swordsmanship in combat strength), or Mihawk simply never fought Kaido.
Either argument can be argued, NONE of it is proven. You can tell me time and time again that Shanks is a 100% pure swordsman and is so because of some dick measuring contest and thus loses to Mihawj, and I can tell you that Shanks has conquerors and can run a Yonko crew unlike Mihawk, and thus its not that simple. NEITHER statement is 100% proven in fact, but its where we are right now in the story.
Like I said, the argument is stupid, there is no fundamental way to tell me I'm wrong, just like there is no fundamental way to say you are. There is no record of Mihawk defeating Shanks. If that was explicitly stated, then you would be right, except it hasn't, so you can't prove it.