You will not need to have any verification of work done, however with that said we do recommend you choose a smog check certified repair shop to make the repairs necessary to get your Mini Cooper to pass the next smog check.
The reason we recommend a certified smog check repair station perform your Mini Cooper's repairs is so that in case of any problems you can have the Bureau Automotive Repairs become involved with investigation the matter. The BAR will not investigate matters relating to emission repairs when repairs are performed at non-smog check certified repair shops.
Furthermore, diagnosing your Mini Cooper's misfire trouble code might be required before simply replacing the spark plugs. The spark plugs might be absolutely fine, and the fault be with a coil pack, coil harness/connection. It would be best for a smog check repair station to first diagnose the trouble code, and then perform the needed repair.
After the repairs are made, your Mini Cooper's ECU (engine control unit) will need to be reset in order to clear the misfire trouble code. Once the ECU is reset, you'll need to drive your Mini Cooper for 100-200 miles over the course of a few days so that the computer's Emission Monitors become READY. Only then will your car be ready for the smog retest.