He is not adding to the damage. Kaido straight up said combined strength of scabbards is not enough to open up the wound because they are no where near Oden. Basically its just surface level damage
But Onigashima going to flower capital, Ryuma dragon slaying legend, Zoro himself declaring he wants to behead Kaido (cut him to pieces), black blade, Kaido seeking glorious death at the hands of samurai suggests he is getting beheaded.
Japanese mythology is full of dragons being slayed by swordsmen/samurai, I doubt Oda would have dragon in a country representing japan, with dragon slaying lore from a man worshipped as a God in it, be defeated with a freaking punch lol