Hey, shielding the cavity won't hurt, but in the short term you should be able to get significant buzz reduction by doing a simple grounding of the bridge. Keavin's way will work (the lug he's describing on your output jack is the sleeve or ground lug). You may be able to more easily access the ground by removing one of the pots (e.g., take off the control knob and remove the big nut that's threaded on to the pot's shaft). Find a big, thin washer that the pot shaft can fit through, then put it on the shaft first, then reinstall the pot in the body. Any exposed metal part of the pot body is ground, and there may have been a lug, but if there wasn't, then you can solder the bridge wire onto this washer. It may be challenging to find a washer big enough and thin enough to work well, so if you don't find anything at the hardware store, you can see if they'll give you a little scrap of sheet metal flashing which you can cut a hole in and use as a ground lug. You'll only need about a 1 square piece, so they'll probably just give it to you.
Once you've grounded the bridge, the strings and your body will act as shields while while you're in contact. The bad part of this is that you can accidentally become part of the AC circuit if there are any grounding issues with your amp or any of the other equipment on the stage. You should take proper precautions, since the line voltage can be lethal! If you shield the cavity of your instrument, it will pose the same potential danger to you.
David Fung