Your NOC isn't hot so you can wait. Also I am not sure whether they will accept your affidavit or not.
In my opinion, since you have received original BC, you write an explanation letter and attach the copy of BC along with and send it to CIO. [Please ensure that translated copy is also included in case the BC is not in English / French - please refer to the guide for that]
In that letter don't forget to mention, your country of birth, your date of birth, your full name, your passport number etc.
All the best