The panel states that Mihawk is "the strongest swordsman in the world".
What did Shanks use when he one shotted Kidd, blocked Akainu and clashed with Whitebeard? Mma fighting? CoC laser beams? A gun? A sandal? No, he used his sword.
The panel states he has better sword skills than an emperor and fellow swordsman, and then restates that Mihawk is, indeed the Strongest Swordsman.