Believe it or not, these rivets aren't all that critical to holding the unit together, so you can be as careful or as reckless as you want (I prefer reckless, because I hate plastic rivets). A good way to carefully remove the rivet heads is to use a flat head screwdriver that is the same width as the recessed rivet hole (4mm?) and "drill" the head away by hand with the screwdriver.
(I used a real drill to do this operation - SG).

Drilling the rivets
The same operation, but in 2D and black&white!

The head is about 2mm deep, so stop "drilling" there to leave the keyboard material shoulder intact for easier reconnection later. There are 6 rivets near the number keys and four above the screen. These rivets above the screen perform more of a holding function than the others, and you may want to consider using some screws and small washers to replace them when you re-assemble.