I presume you are well aware of the many cautions about not removing the Vin plate. I just mention that in an abundance of caution. For the record, those rivets are said to be very special, having a unique dome to them and now longer available. That makes them one of the keys to originality. But ultimately it is your car to do with as you wish.
Good luck, Gene
PS: I am belatedly thinking I may have missed the real question. Perhaps it is how to get out the back side of the rivet if it would drop down into a blind cavity. No real answer for that. But, I doubt they have enough substance to make a rattle, at least one anyone could hear with my exhausts!