I see you have an 08 Z. Some 08's are having cat failures. Mine did at around 2000 miles. You will have to take it to the dealer to get checked and code cleared. I have my exhaust fuse out also, but that has nothing to do with it. I had them clear the code and waited to see if the CEL came back on or if it was a fluke. Came back on two weeks later. Had right cat changed. So far so good.
On a C6 you need a code scanner with CAN capabilities to reset the light or get the codes. You can get one at any parts store for under a hundred bucks. Since you probably have warranty your dealer is your best bet. You will not get a code by pulling your exhaust fuse.