Just to bookend this one....
Cherry had a video on their website that recommended using a center drill to drill out the lock. This worked for one rivet but I couldn't make it work again.
I ended up using a cone shaped grinding stone in a Dremel tool. ( This stone likely came with your Dremel kit and has been collecting dust for 10 years while you wonder what it's good for. Well, its good for this.) This is delicate surgery for sure, but with a little patience you can dish out the rivet head a sixteenth or so which allowed me to punch out the stem.
If you have to do a lot of these I would find the pilot at your airport that's a dentist ( there's a dentist at every airport) as he likely does this every day.