I believe that Itachi's Totsuka Blade is actually not really a sword. The Totsuke Blade is a sort of liquid released from the gourd that Itachi wields and only forming into a blade like shape (according to the wiki at least)

https://naruto.fandom.com/wiki/Sword_of_Totsuka

Plus I think it would be weird to call Itachi in his Susanoo form a Sword Ninja since I would only consider ninjas with an actual metal blade a sword ninja (including Orochimaru who has his snake sword stored inside of him, he's not using it with his hands most of the time though).