"And because the increadible speed he moves at. It emits a distinct chirping sound similar to a thousand birds chirping. That is why that move is called Chidori." This is what Gai told us about the Chidori. (Chidori = Lighting Edge / Strike). So what makes the sound is the increadible speed. So the answer to the guestion why Kakashis move didn't make that sound is that his speed wasn't fast enough. And as we saw, he didn't have to reach a huge speed to kill Zabuza, so why to waste chakra? His hand went through Hakus body with the speed he had, and that was enough to kill, so no need to get a huge speed... I hope you are happy with that answer?