The classical theory of radiation tells us that a particle emits radiation whenever it is accelerated. But in our model the CC is constantly moving in a circular motion and thus it is always accelerated. This means that it is the acceleration of the CM the one that matters regarding radiation.

The theory of radiation has to be rewritten.

Our free particle conserves its kinetic energy but its CC is accelerated, so that no radiation has to be associated to an accelerated CC moving at the speed of light whenever the CM is moving at constant velocity.

The electron cannot decrease its CM velocity spontaneously. Just consider the analysis by the CM observer. A free electron cannot emit radiation.

Radiation has to arise whenever the CM is accelerated and its velocity decreases, so that we need both, an external accelerating force or impulse and a decrease of the CM velocity.