My husband has a paralyzed vocal cord - from a surgical procedure which used a very large breathing tube (so it wasn't thyroid surgery). At first the cord was paralyzed in the open position, so he was hoarse and he choked when he tried to eat solid food (since the cord was in the open position, then the trachea (tube to his lungs) was not sealed off when he swallowed) - it was so terrible, he lost 40 pounds and he wasn't overweight to begin with!
Finally, the paralyzed cord moved to the center position so that when the other one closed (during swallowing) then he didn't choke. Also, his hoarsness improved and he only is hoarse from time to time.
They said that he didn't need a surgical procedure - so I'm not sure how his paralysis is different.
I hope things go well for you. It is scarey to have a paralyzed cord!