You are totally safe with a cat back exhaust. You can even get away with headers, down pipe and a high flow catalytic converter. Upstream before cat and downstream after cat O2 sensors need to present and working. Car can't have any codes.
Honestly OBD 2 cars run better with emissions in place. I was big into the custom compact scene in the late 90's early 2000's. I ran an
emissions legal header, moved close coupled cat with a custom down pipe to under the car with a high flow cat. Finished this off with a cat back exhaust. Setup made a big difference and the car passed emissions and had no codes.