I don't see how the problem could get worse by doing exercizes. The cord is long enough to go around the neck and then some, and if there are going to be any issues, it will be at birth, not before. Some babies are born with the cord wrapped entirely around their bodies several times.
The problem with cord around the neck or around anywhere is that if there is too much pressure on the cord it could cut off the blood/oxygen supply to the baby. The baby is not breathing through its mouth at this stage so the cord isn't going to strangle the baby or anything like that. Some babies might have particularly short cords or the loop might be very tight, or there might be multiple loops, which is why for some babies it is a big deal. A knot in the umbilical cord also happens, and that is a big deal. They need to be telling you why your baby's nuchal cord is so much more dangerous than that of the other 1/4 babies who have one.
AJR, would your wife consider going to another hospital for an ultrasound just to get another opinion on the whole nuchal cord thing? It sounds like yours might be a bit of a fear monger. Very typical with Chinese OBs, unfortunately.