Look I’m an admiral fan so I know a bit about being delusional, and trust me, when I say Mihawk fans are THE MOST delusional people I’ve ever talked to, I mean it.
No the story proves other wise actually.
Oda through his story has made it abundantly clear:
Every single individual classified as a top tier for the pirates was a swordsman lol.
Gol d rodger = swordsman
Whitebeard = main form of fighting was a blade that's a Supreme blade
Shanks = Swordsman
Rayleigh: swordsman
Ryuma = swordsman
Oden = swordsman
Coincidentally everyone of these "Swordsman" are also Haki monsters. The entire premise of cursed swords was debunked in story and now we realized that the user of said supreme blades must overcome the swords will, thus the wielder must impose their own will upon the blade. This hints to the wielder having to have huge amounts of will = haki.
Yet for some apparent reason the individual stated in story to be the greatest swordsman in the history of onepiece doesn't have impressive haki even though impressive haki as shown is the height of swordsmanship in the verse?