But if swordsmanship is your most powerful ability - which it wasn't in King's case - other abilities don't matter. If Mihawk is superior to whatever Zoro's swordsmanship can produce (Shishi Sonson, Dragon Damnation, Asura, amped by ACoC), then giving Zoro King's lava-like Dragon won't tip the scales either. Mihawk won't lose to a flame dragon if he is strong enough to defeat Zoro's Asura.
Same goes for Xebec. He doesn't have a Devil Fruit or fancy abilities, just a sword and Haki to use both shockwaves and cuts. We also know Shanks had access to Kamusari before being rival to Mihawk, so Mihawk accepted a rival with shockwave based abilities.
I believe
@Salah WG pointed it out too; characters are basically as strong as their strongest move. If a sword users strongest move or ability is related to swordsmanship, then it doesn't really matter what else he is capable of.
Swordsmanship is Defined by People, it basically means "Any Peformance involving a Sword",
Swordsmanship is like showcasing what is Possible to do with a Sword,
If Zoro sticks his Swords to a Huge Rock & Attack you with it, that's still Swordsmanship,
If Jean Ango throws a Sword at you, that's still Swordsmanship,
If Cabaji spins his Sword at the Ground to create a Dust Cloud, that's still Swordsmanship,
If Brook channels & releases his Soul through his Sword, that's still Swordsmanship,
If Law controls his Sword from a Distance & make it Attack Someone, that's still Swordsmanship,
If Big Mom swings her Sword at Hera/Prometheus to shoot their Combined Energy, that's still Swordsmanship,
If Shanks channels his Haki through his Sword, that's still Swordsmanship,
If Shamrock's Sword transforms into Three instead, that's still Swordsmanship,
If Tashigi let's a Cannon Ball land on her Sword so She can redirect it, that's still Swordsmanship,
... etc
Swordsmanship isn't a Fixed Set of Techniques, it simply refers to People's Preference of using Sword as Medium in performing whatever Task,
"Anything" that can be done with a Sword, can also be done without, even Cutting can be done with Legs or Hand Chops, and thanks to Haki, you also don't need a Sword to Clash with anything,
So, when does it become Swordsmanship? Simply when you choose to do those things through a Sword, that's all.
Meaning it's not about what you Produced, it's about which Weapon was used to carry that Production, as Simple as that.
Being Greatest Swordsman means that what Mihawk can Produce (What Fuels his Fighting-Style) is Top 1,