Not every sword user considers themselves a swordsman.
This was confirmed with King, who while being extremely skilled with the Katana, used a mixed fighting style that combined punches, kicks, and his zoan powers.
I think it is extremely likely that this is Nasujuro's fighting style. While Nasujuro no doubt has a katana, when he actually needed to fight, he turned to his DF powers.
Nasujuro clearly seems to be a mythical zoan. His form looks exactly like Luffy's gear 5th, indicating that this is some form of mythical hito hito no mi.
If we look at how varied and free flowing Luffy's fighting style is in G5, it just makes no sense for Nasujuro to be a traditional swordsman if he has a similar DF.
Anyways I bring this up because a lot of people are using the existence of characters like Nasujuro to claim that Mihawk is a fraud, which imo is slander. Similarly, a lot of Zoro fans are opposed to Nasujuro being Zoro's final fight, despite the chronology heavily suggesting it, out of fears that it would make Mihawk fraudulent.
However, I think if you look at how Nasujuro is set up, you will see that this is the complete opposite from the truth. Rather than being some sort of shadow WSSM that proves Mihawk fraudulent, Nasujuro is portrayed as a DF master, wielding an awakened mythical zoan. While his style will definitely incorporate swordsmanship, the focus is on Nasujuro's DF, not his sword. That's why he doesn't have a black blade.
In his fight against Mihawk, Zoro will prove himself to be the world's strongest swordsman. However that isn't his full dream. As with Luffy, Zoro has a secondary dream.
Zoro doesn't want to merely become the greatest living swordsman, he wants to be such a great swordsman that his name will even be known in heaven. The only way for Zoro to have his name be known in heaven, is for him to defeat a god. In his fight with Nasujuro, Zoro will do this very thing. He will slay a god and become known, not merely as the greatest swordsman of his era, but of all time.
