Is your life worth playing legal games over? I don't know the technicalities, but I do know that in the event of an emergency they will bring that copy to the hospital and lock you down. Who is then going to show up with some other documents rescinding the no blood mandate? Will they stand a chance when Witness after Witness to your JW affiliation says that they saw you sign the card, saw you at the meetings, etc? What if you need blood now and it's delayed for a legal fight?
Don't sign the card or give them copies. That would be my stance if I had to stay in. Your life isn't worth any of those people.