A question to make Aristotle bite his fingernails. Maybe it's something we can't "really" know until we're faced with it, but my most truthful answer would be no, I wouldn't respect her wishes.
Many years ago, a car ran a stop sign and pushed my car into a cement bridge. Most of my bones were broken, organs ruptured, etc. It was bad. My parent's are JW's. I left home and the religion as soon as possible. Was never baptized. They knew how I felt and knew I didn't accept their stand on the blood issue.
My husband was killed in the accident, which left decisions to my parents. Knowing that I wouldn't stand a chance of living without blood, my mother said no. They told her they would get a court order but my time to live was severely limited and the time it took them to get the order might make a life or death difference. She refused. They woke a Judge and got the order.
Though she said "it was the hardest thing she ever did," saying no, she had no choice. How does someone say that about their child? How does someone put a humans word that the Bible means what they say it means ahead of a life? How does a person put fear of disfellowshipping ahead of their child?
I don't know, but feel pretty sure that I'd sign for her to get one. Not from any sort of "payback", but simply because I couldn't live with myself knowing she died because I wouldn't sign that paper.