You kind of defeated your own argument here, bruh.
King never claimed to be a traditional swordsman who focuses solely on his sword.
That would be like Zoro mixing his 1, 2, and 3-sword style with hand-to-hand combat no sword style regularly but he doesn’t, because Zoro follows the Wano way of the sword.
King, on the other hand, fights in his own unique style. Just because he doesn’t follow Zoro’s definition of a swordsman doesn’t mean he isn’t one. Not all swordsmen in One Piece stick to Wano’s swordsmanship code.
For example, Kaku uses Rokushiki mixed with his sword techniques, yet he’s still called a swordsman. King is even referred to as the “Masked Swordsman” in his Vivre Card.
The idea that King isn’t a swordsman is Zoro’s own assumption not something King ever said himself. King never denied being a swordsman. Zoro assumed King wasn’t one because he used other abilities, but that’s Zoro projecting his own belief of what a swordsman should be