The holes for the rivets are 5/64".
I doubt that a 'Dremel', will allow much room to grind; a long half-round chisel (cape)
or a large rat tail file might just do the trick however. (in from the head tube)
The remaining portion of the rivet may be driven out with a long punch carefully used,
alternating from one end of the tube and then the other end. (light taps)
'Pop', brand rivets are both too large and do not give the 'look', that you desire.
Small screws or 'drive-ins', (preferable) would secure the badge.
Regards,
J T