Haki is part of being a swordsman, just like your strength, speed, and everything else is. That's about as retarded as saying "He is very speedy... so he's not a swordsman- he's a speedman!!!"
"THIS DUDE IS NO SNIPER! He has CoO! He's observation-man!!!"
God.
And are you really using minor use of hands or feet to say some character who primarily uses sword is not a swordsman lol. Kicks are irrelevant- King sits here with a whole devil fruit and fire creating technique- that's what separates him, not that he can kick things much like literally every character with legs including Mihawk and Zoro.
CoA and CoO are base tools, adv CoC is something else.
Adv CoC acts as a buffer between you and your opponent, it is antithetical to pure swordsmanship.
Kick's kings aren't minor, Rayleighs kicks saved Zoro's life. Sai and Judge use a spear and kicks, I wouldn't call them pure spearman. Kicks are all Sanji uses and he is on par with Zoro, so they aren't to be discounted just because you are a zorotard.
I don't see Mihawk incoporating brawling into his sword style and don't think he has adv CoC tbh.
I think Shanks and Mihawk had swordsmanship duels but Shanks' actual combat incorporated kicks, then he learnt adv CoC while becoming a Yonko, after he stopped dueling Mihawk. You cannot debunk this, we will have to wait and see, but that is the argument distilled as to why Shanks is not just as swordsman.