In theory you could do this but I don’t know what the procedure would be.

Under the normal Swiss system you arrange cover and give evidence of this to your commune. If you change insurers, which you can do by the end of June or December, you apply to a new company and serve notice on your existing one that you are leaving. Your new insurer will issue an attestation that they have assumed the risk and once your old company have this you are released from them.

If you have a policy which is outside the normal system it should have been approved by your Canton and some sort of confirmation issued. If you then apply to a normal Swiss company you would have to explain why you have been in the country without normal cover so I presume some sort of document from the canton would be necessary to show that your position has been correct.

It’s not a procedure that I have know anyone to do so I have no experience of this. If you attempted it you should contact the canton and the new insurer in plenty of time.

I’ve assumed here that you have an insurance which is outside the normal system and approved by the canton. If you were relying on one that had not been approved that would be a different matter.