I think it should because we saw Loki kill Harald and though this feat has an asterisk the possibility of killing a HK stands. And when you consider that the lethality factor is highest for swords then the required AP should be a possibility for the WSS.
I have told my views on the WS titles before but the gist is that the eras are different for all three. And because we haven't seen them defeated hence their title stands. Kaido being stronger than WB individually is canon as per Ace Novel. And the titles of WB and Kaido are tied to their fruits too. WB because he can destroy the world and the reason why BB proclaimed himself the strongest after eating the DF. And Kaido because of his invincibility and a guardian diety DF. And these guys have top tier individual strength too instead of being just DF merchants. You can notice how their strength is again highlighted in the Road to LT magazine where the weapons and their grades are discussed and how their weapons are able to channel their full strength without breaking. And this is also the reason why I think Mihawk has more AP since his weapon is the strongest and toughest/unbreakable to channel his max strength without breaking.
And lastly Venusjuro has more claim in this argument since his level of seal is even higher than the HKs supposedly.
Loki killing Harald has no asterisk because before it did happen it was stated only Loki with DF can actually kill him. Harald letting himself be hit has no relevance to Loki attack overcoming regeneration which is passive ability .
Yes you yourself confirmed titles are because of their devil fruits and not because they defeated everyone noteworthy in the world. Seeing how Kaido can turn into a dragon and is Oni no wonder he was given strongest creature , and seeing how WB can literally destroy island no wonder he got WSM title. They were given titles because people considered them strongest .
It doesnt matter MIhawk is from different era , he never did anything noteworthy that would cause people to consider him WSM / WSC instead of those 2.
Mihawk title may be the most legit one because he did actually want to become WSS and was defeating his opponents for that. Yet we also know he did not fight every swordsman outthere . We know he never fought Vista , most likely Fujitora too and for certain he was not facing Shamrock in his quest for becoming WSS.
Unless Oda makes him regeneration merchant like rest of HK and Gorosei for me Shamrock is Shanks with both hands ( manga literally stated their talent / potential is equal ) plus Imu buffs with Cerberus sword .