Damage control /\ using exceptions as rules
Manga has already confirmed, you are a swordsman if you use the sword as a FIXED fighting style. If you use other tools then you are not a pure swordsman, confirmed twice in the manga by Daz Bones and King
How's that exception when he carries that pocket knife around with him. That wasn't around a weapon he just found and picked up. If it was Zoro using a scythe then maybe you coukd use that as an exception because Zoro didn't plan on using the scythe at the beginning of the battle.
Don't be upset because you can't properly comprehend the manga. Kaku uses kicks and yet he consider himself a four sword style swordsman. Legs are not swords and kicks are not sword attacks. None of the other CP9 members considered their storm kick attacks sword attacks. During his battle with Zoro he wasn't even able to use his swords because of his new devil fruit battle yet he never stated he was no longer a swordmans. He was limited to just using his limbs.
What you and so many people don't understand is swordsman are not limited to just using swords and there's different types of swordsman. They aren't all the same just because they are swordsman. Zoro stated he would rip out Kings windpipe if he has to to win. I don't see Mihawk doing that because of type of person is but that doesn't mean Zoro isn't a swordsman just because he will. That shows how they are two different types of swordsmen.
If Oda didn't want King to be a swordsman he could have had King said "I am not a swordsman". He had the perfect opportunity to say that but he didn't.