I also had an emergency CS but wasn't strapped down. Mine was a bit of a rush after a failed induction and DS being stuck with a posterior lip, I think all in all it was 45mins from the time it was decided to when DS was born. The aneathisist (sp?) was holding one of my hands (probably so she could monitor the IV etc) and DH was holding the other. As soon as DS was cleaned up he was put on my chest so I could cuddle him. So I would definately talk to your OB and make it clear that you don't want to be strapped down.