The way I always understood the basics of Chidori was that it basically just concentrated an insane amount of chakra in one place (so much that it became visible). How the chidori was used was the thrust and the assassination technique part. The Chidori Nagashi seems, to me, be Sauke concentrating a huge amount of chakra surrounding his whole body. The blade its likely what others have said, Sasuke using the huge amount of chakra of chidori and putting it through the blade instead of into his palm.