Oda gave King multiple fighting styles and different abilities like a DF and Kekkei genkai to justify his overall strength. You can apply the King rationale to the likes of Kizaru or even Fujitora for that matter, but not to peeps like Shanks, Rayleigh, Roger, etc.
I agree that they are definitely swordsman but like I said earlier the Shanks Ray, Roger kind of swordsman are in a different lane than Mihawk, Zoro, Ryuma etc.
Shanks will be using haki blasts and the like, his swordsmanship will be a lot cruder, as will Roger's. They don't care to cut cleanly, or precisely. They are just going to stack all their haki mastery and let it out in their attacks. You will never see Zoro or Mihawk shoot out haki barriers around their slashes because they will always want to make direct contact, they would be nerfing their own blades lethality if they did. They attack with a specific purpose, to cut. Everything they do is to enhance this property.
Mihawk sends a slash at Luffy, Daz blocks it, Mihawk adjusted the potency of his cutting property to slice down Daz. He may have done the same for Jozu. Someone like Shanks is just gonna blow Jozu up with a haki shockwave slash, I can guarantee you will never see Mihawk doing this. He will always rely on his cutting prowess cause that's what his fighting style is centered around. He will "cut" diamond, Shanks will destroy it.
The WSS title means Mihawk has taken swordsmanship to its peak. Even beyond Roger, you won't see Roger with the same cutting feats or a black blade, but this doesn't guarantee he is below Mihawk.