Hakiman is not a canonic style. Regardless haki is integrale part of swordsmanship in some forms. It works as accessory.
Sure CoO and CoA are apart from swordmanship, but something that only the very strongest can use doesn't sound fair to swordsmanship.
Creating lighting, barriers is not apart of swordsmanship. which is skill with your sword not conquers haki.
+ I think it's kinda clear shanks got stronger from his mihawk duels.
He went from a regular CoC blast on the seaking, to using his conquers continuously and we know conqeurs can't be trained it's get better as you get stronger.
As for mihawk getting stronger idk, but there still =