^^^Yeah, something like that was what I had in mind also, as far as clasps are concerned, although would need one/each drawer of course.
Another thought is you could run a drawer lock (the round key type as mentioned) where you drill a hole thru the panel, push this thru and it has a locknut on the back side to go against the backside of the panel (drawer)..it has a lever that rotates 90 deg so that it goes up against the top (or side) part of the drawer (fixed part), so that you can't open it.