Which exhaust with emissions?

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.

It took at least 25 years for most car manufacturers to figure out how to get back the power lost with emissions. Then they ended up making more power because of them.