Since we are dealing with the Ororchi...how a bout the grass cutting sword? the blade Sassoon found in its tail that was finer even than his godly sword? Perhaps the sword was in fact the tail/body of the snake or contains its power at least?

EDIT:

Though do keep in mind just because this is Inuyasha inspired this game does have to have a One to One plot point mirror of the Inuyasha story.