Battery Disconnect Switch: Shank Diameter

I'm pretty sure the way these are supposed to work is you put an eyelet type connector on the end of your battery wire then attach it with a bolt through the hole you can see in the first photo (on the end where you are trying to connect the clamp to). The new clamp replaces the old. The green knob is there as a quick disconnect. You unscrew the green thumb wheel and then the wire is disconnected without taking the clamp off the battery.

In short, cut off the old clamp and put a new eyelet in its place. Something like this:

You'll have to figure out the correct size for both the cable (awg size) and the eyelet size for the bolt connector.