You can certainly drill, but go slowly as the heat from the drilling can damage your plastic (experience talking). Also, watch out for the rivet being loose as it can spin while you drill and also cause damage. Certainly not impossible, but just go slowly.
If if you have a dremmel, that's even better, you can grind the rivet out with a little better control.
Update: After further examination, it appears the "metal rivets" are actually melted plastic pins.
Therefore I tried to heat up the piece to remove it to no avail. I drilled out two of the rivets, but the hard black plastic piece is not lose at all and appears to be glued or sealed.
I've decided to just leave it for now and hopefully find a shell some day to experiment on it...