I am asking you who dud Fuji cut since your claim you need to cut
He didn't have a chance to cut someone i suppose.. He did cut and blinded himself though..
But if you want my opinion on Fujitora, from what we've seen, i wouldn't consider him a Swordsman either..
If he has an attack in his repertoire where Gravity literally starts piercing, slicing or cutting people up, then i would consider him a Swordsman..
Edit: Or if he has a Swordstyle..