You can proceed without the oil. The crust will be more like the "elite" NY style that uses no oil or sugar. If the dough has pretty much been made, I don't think I would add the oil and mix it in. Instead, you can coat the dough balls liberally with oil and some of that oil will eventually make its way into the dough and also at the time of forming skins. You could make breadsticks out of the dough but there is no need to do that. You definitely should not throw the dough away. It will be OK.