In researching your question I came across several jeweller sites that claim that with proper technique you should be able to remove the screws without damage.
However I found this unsatisfactory, so I dug deeper, and the answer is yes, there exists nylon bladed screw drivers
Those could be screws with the heads removed, specifically to prevent people from opening the device. In that case, try to cut a slash across the top of the screw so that you can get a flat-head screwdriver in there. A dremel comes to mind, although you'll damage the plastic casing, but, hey, if you want to make an omelette...
Just as likely though, they are like ring-shank nails, with notches on them designed to catch on the plastic inserts on the other side and ensure that they never, ever get removed without destroying the device. In this case, the answer may be to drill the head off of them so that the shank can be pulled through the hole in the plastic. Understanding, of course, that you won't be able to put them back together.
Best Answer
You need a pin wrench (or pin spanner).
They come in fixed and adjustable types.