A surgery might cure a vocal cord dysfunction, but there is no guarantee at any time with a surgery. Some vocal cord dysfunction could be helped with exercise or rest.

No

Diaphram breathing, temple massages, throut rubs

Tightening of the vocal cords is also known as vocal cord dysfunction (VCD). This is a condition in which the muscles of the vocal cords tighten and this can make breathing difficult. It is caused by an autoimmune disorder.

It depends on what type of surgery your inquiring about. If it was medically necessary surgeons would probably find a way to work around it.