Its unlikely that you will be able to do this. Usually the glovebox is a complete unit that is fitted to the IP during production build. I don't have access to MB service information, but I do work in the industry in an area where we have lots of involvement with Glovebox development and assembly.
Normally the whole glovebox would be the servicable item that you would need to remove.
No experience with CLK but this is the case with W210, W203, W204 and W221 (the models I have knowledge of).
Best way to confirm would be to contact your dealer to see if its possible to buy a glovebox lid only, if not then you probably can't remove it.