I disagree. Why would a battle between swordsman be so much different to battles in general, where characters with weaker haki perfectly have the ability to damage and even defeat their opponents?
Ask Oda.
Pica was certain that he could beat Zoro if he has a better Haki and Zoro agreed with him on this idea.
I think that Oda introduced the concept of « a nik on the blade is a swordsman’s shame » to use a swordsman having his sword broken as a cue to his total defeat. Thing is that all the competent swordsmen put Haki on their sword which means that if you are not able to bypass your opponent Haki, you cannot cut their sword and thus you cannot defeat them.
Broke the sword of a swordsman is breaking his spirit. Which is probably why Oda had recently introduced the idea of « the beloved sword of » (thing that did not exist preskip).
For example you can say that Kinemon’s spirit was broken when Kaido destroy both of his blades.
This concept was also expanded with Shusui because the people of Wano thought that it is because Shusui was stolen that the island was suffering is current fate, as if losing the sword defeat the will of the samurais. The belief is so ingrained in them that Hiory gave away her heirloom to get it.
We can furthermore talk about the fact that in Wano every samurai has a sword made for him at his birth and his buried with it. Stealing one of this sword is seen as something blasphemous.
Reinforcing the idea that the sword is link to the swordsman on a spiritual/soul level.
Therefore the swordsman as to do everything to protect their sword which is why every swordsman in Wano knows how to flow haki from the body to the blade.
In this line of thought we can think that making a black blade is the testament of an unbreakable spirit/will forged in countless life threatening fights.
One step forward, and the conclusion is that Mihawk spirit/will is stronger than Shanks.
Obviously I can be totally wrong about all that but if making a black blade is link to spirit/will in any shape or form, it would seems obvious to me that the logical conclusion is that Mihawk as a stronger Haki than Shanks.