Suggestion to electrically disable a Faraday Cage
The following is just a guess.  I could be completely wrong.

You can't disable a cage, but you might be able to make a switchable "leak" in the cage.

Imagine this, you have a cage with two antennas.  One antenna on the inside, one on the outside.  The two antennas are connected with a wire.  Where the wire goes through the wall of the cage you place a switch (or relay, or whatever).  If the hole in the cage is smaller than 1/4th wavelength, and the switch effectively prevents the signal from penetrating the cage, then you might just have something.  

You might need to do some fancy shielding around the hole and switch, to prevent leakage when the switch is off.  You might also consider connecting one or both antennas to the wall of the cage when the switch is "off".

It probably won't ever be perfect, but it might do what you want.  Unless you are a forigen spy, intent on disabling our security in sensitive military complexes.  Then it won't work.  For that you need to know the secret combination, which is 1234 by the way.