In my experience with drilling out rivets, I have always started out just slightly larger than the mandrel on my drill bit diameter, and run that thru. If its a 1/16″ mandrel, I run a 3/32″ drill bit thru. 1/8″ mandrel, I will run a 3/16″ drill bit thru. Typically this is enough to weaken the body of the rivet and once you get thru it will separate the back side of the body from the head. If you run thru and don’t break the rivet, go up to an 1/8″ drill on the 1/16″ mandrels, and go to a 7/32″ bit on the 1/8″ mandrels. Doing it in steps like this will allow you to replace the rivets with the same size as you will break the rivet without ever touching the glass with the drill bit.
If when you get them drilled out you find that a few holes have enlarged due to accidental damage or some other reason, you can always upsize to the next rivet, but if you don’t have any damaged holes, you will be able to reuse the same size rivets.
The unknown factor in this scenario at least from my side is what is behind the wall you are drilling. If the cavity is filled with insulation, getting the back side of the rivet off the drill could be problematic as you don’t really have a good way to pop the body off the drill bit. If it is open behind the wall, you have a better chance of pulling and getting the body free from the drill bit. If the rivets go thru a wall and into the next compartment, you are golden cause you can grab the body with a pliers and peel it off the drill bit tip.