Well, the idea behind the "click" is that the sound is always the same. The click lets the dog know that it did something good at that very moment and will be rewarded for it. That's why I think it's better to use "yes!" if you choose not to click.

Clicker training is training step by step. So instead of having the dog weave all the way, then rewarding, you click (or say "yes!") when it enters the correct side. After the dog starts getting it, you only click when the dog takes a step out, then click when it goes further and further. The idea is that the dog will start offering things (another step) to you in exchange for the click.

It's a bit of a hassle to introduce the dog to the clicker/method but I've found that Kai's weaves were 100% more solid after I started clicker training.