Just take the one that goes inside the wheel out. Leave the first one alone, it aids in clicking the scroll wheel down.
If you have the Dell mouse that i'm using, you'll notice that there are two springs, one wraps around the post in the center of the wheel, and one is situated in the small plastic piece the wheel rotates around. Now, instead of breaking all of the spokes out, we'll just take the little spring that hits each spoke as you rotate the wheel. These spokes are the reason for the clicking. If you look carefully at one side of the scroll wheel in the non-optical mouse, you'll see that it's spoked.
