A couple of suggestions. First never use foam packing peanuts. They are static generators.Stick your arm in a box of them and you'll see what happens! Use peanuts made from corn starch if you feel the need to use something. Don't use regular bubble wrap. Use the pink bubble wrap. It is used for electronics. Better yet is the pink zip lock bags which are also anti static.
Grounding is not as important for LOW power signals. Even a signal in little old Kilowatts can leak into your cage if it is NOT grounded. Cell 'phones and key fobs are very pow power devices.
On another note, if you have a COMPANY cell phone, you need to have a small Farrady cage-like a candy tin to put the 'phone in when you are not on the clock. I knew of several people fired because the boss said they spent too many hours in the beer joint when they were on their own time!