I wouldn't risk letting it out of my sight. The hard drive will be under a cover on the bottom of the case, usually two screws. Drive is held in with one screw. Slide it out. Write a note saying why you've removed it and put the cover back on.
Did this for a friend a couple of weeks ago, and we've heard nothing back, if they ever opened it up I'd be very surprised.
If you want to either borrow an adaptor or send me the drive to get the data off onto a cd/dvd send me a pm.