If I understand correctly, you should bill Medicare first (electronically if you can) for the denial, then send to the secondary. That's the same as if the provider were par with Medicare. HOWEVER, you have to be registered with Medicare to bill Medicare, Par or Non-Par, otherwise they don't even know who you are and will throw out the claims.
I'm not sure that the doctor can even see a patient with Medicare if they don't bill Medicare. The patient would pay at time of service and submit their claim themselves. One of our urgent care facilities does not participate with Medicare and that's how they handle it.