If you use a sword as your main weapon and it is also the main tool for most of your offensive and defensive techniques, you are a swordsman, REGARDLESS of whether or not you add the "sword style" tag to your attacks.
Law - Law is the most complicated to classify, because approximately half of his attacks are using the sword and the other half without it. Furthermore, his akuma no mi has abilities that are completely foreign to the world of the sword, but he also benefits from using a sword to cut or divide his rivals, also, in his awakened form, which he mainly powers and his most powerful attacks are with the sword.
Hyouzou - For albino, Hyouzou is not a swordsman, since he does not use the "sword style"
Kyros - Another character who, for Albino, is not a swordsman, since he never mentioned being a swordsman and the only technique we saw him use is called "Trueno bastard". No "sword style"
BM - As I have found, BM has approximately 16 techniques, of all of them, only 2 or 3 are using the sword. And furthermore, even when blocking or defending himself, she barely uses it or on no occasion do we see him do it. Everything else is punches, lightning attacks and fire.
King - Similar to BM. Most of his attacks do not involve the use of the sword, he uses fists, kicks, the power of his akuma no mi, the power of his race, flames and lava, etc.