If we are to describe things in characteristics and specialist terms, then I think there actually is a particular way to look at this that makes sense.
The World's Strongest Swordsman title is the same thing as saying the King of Swordsmen. If we put it into those terms, then the Black Blade is the trademark characteristic of this character type.
I believe a characteristic of Conqueror Specialists is that they have a powerful soul. Prior to being able to use Conqueror Haki, Armament Specialists are just considered typical swordsmen.
That "powerful soul" part is what makes the Black Blade. It's temporary with only Armament Haki because it's not powerful enough, but when Conqueror Haki is infused it causes the Armament Haki to become amplified. It's still the same thing as before, it's a matter of residual energy, but it never reaches a critical point until a swordsman has Conqueror Haki.
This wouldn't indicate that the King of Swordsmen is the strongest Conqueror Specialist, but it does mean a powerful soul is required to be the strongest swordsman.