I would like to add that after what Shanks did to Kid, Mihawk being stronger than Big Mom is easy to believe
At this point, I think it's insulting to put BM above any "top tiers" except the old trio (Garp/Ray/Sengoku) and the new admirals lol.
It's more likely that, as the manga has been implying, the two are equals.
Shanks is the lesser swordsman compared to Mihawk. That can no longer be questioned given the fact that it is seemingly a publicly accepted fact given that panel with the marines.
By that same token, that evidence is clearly based on their past duels, seeing as how they stopped fighting when Shanks lost his arm. The same duels that they've never officially settled. So, apparently, despite it being obvious that Mihawk was the better swordsman back then, Shanks was still doing something to stalemate Mihawk, who couldn't overcome the now Yonkou. And despite this mysterious something, Shanks also couldn't overcome the now WSS.
And I think we are supposed to take that "swordsmanship" statement at face value and consider them to be referencing just the skill itself. Imagine if that statement read "Yasopp has better marksmanship than either Shanks or Mihawk!". We'd take that at face value without immediately jumping to the conclusion that Yasopp's CoO is better than either of theirs. We can assume that haki is just as applicable to Markmanship as Swordsmanship at higher levels, but Markmanship itself is the main skill being focused on.
Regarding Shanks/Mihawk, I think the following makes most sense IMO;
- Mihawk was famous when Shanks started dueling him, and Shanks got his fame from dueling Mihawk. This implies to me that Mihawk was initially stronger than Shanks, but Shanks eventually closed the gap to the point where the gap was pretty much non existent and they started stalemating each other over their many duels.
During this time, there was no definitive strongest swordsman, so Shanks stalemating Mihawk has no implication on Mihawk currently being WSS.......because Mihawk wasn't WSS back then based on our knowledge (at least there is no confirmation regarding this).
- Shanks probably had more potential than Mihawk, and would've eventually surpassed him after some years. This makes sense to me, since IMO 2 armed current Shanks would be Roger. But then he lost his arm, betting his potential on the new era, symbolized with passing on the Strawhat.
This is also why Mihawk is stated to be waiting for a swordsman surpassing his rival Shanks.
2 armed Shanks (hypothetical) >= Mihawk >= Shanks
- Yassop being a stronger marksman than Shanks/Mihawk would have some implication on haki, if Shanks/Mihawk were also marksmen. But since they
aren't, this is like comparing apples to oranges.
Anyway, I get the point that swordsmanship has skill involved in it. But ultimately, it is
both skill and haki, with haki playing a bigger role from what we have seen in the series. There is a reason why ALL of Zoro's powerups post timeskip was with his haki, there is a reason why the first thing Mihawk taught Zoro was haki with specifically saying that even a scratch on the sword is an insult to swordsman.
The world's strongest swordsman is simply that - stronger than anyone in a swordsfight, haki included. Yes, WSS doesn't necessarily need to have the best haki amongst all swordsmen, he just need to be strong enough overall to be WSS (meaning haki + skill + physical stats + whatever else, "overall power level" should be the highest)
I personally believe that Shanks has stronger conqueror's haki than Mihawk (he's pretty much confirmed to have it through Zoro's ambition being confirmed a conqueror's ambition), while Mihawk have stronger armament and observation haki, making the "overall power level" slightly higher for Mihawk.