"cosmetic operation" is correct and usable in written English.
You can use it when describing an elective surgical procedure that someone has had done to improve the appearance of a body part. For example: "After years of considering it, she finally decided to get a cosmetic operation to reduce the size of her nose."
She hopes to have further surgery before a final cosmetic operation.
Rib removal is a questionable cosmetic operation, often performed with abdominoplasty ('tummy-tuck') to give a person a thinner waist.
Almost two decades after a national hue and cry arose after fears that leaking silicone breast implants might cause systemic disease, breast augmentation has become the country's most popular cosmetic operation.
More mysterious objects included a pantomime horse, a pair of breast implants left by a guest who was en route to London for a cosmetic operation, a script for a soap opera, a box of 200 Queen Elizabeth masks and a wand - worth £2,000 - that was used in the Harry Potter films.
In fact, she refers to the cosmetic operation as "the best decision I ever made".
The bottom line is each cosmetic operation or procedure carries specific risks that can be extremely harmful.
A few obscure cosmetic operations increased in 2009, despite their not-insignificant cost.
The number of cosmetic operations in 2009 fell by nearly 9 percent, according to the American Society of Plastic Surgeons.
Last month, the American College of Obstetricians and Gynecologists warned against cosmetic operations for the vagina.
Last year, according to the Society for Aesthetic Plastic Surgery, 1.8 million cosmetic operations were performed in the United States.
On television, reality shows like "Extreme Makeover" and "Dr. 90210" normalized vanity medicine, making cosmetic operations seem cuddly and carefree.
