Who operates to fix sports injuries? What type of surgeon do I need for a sports-related skeletomuscular injury?

Orthopaedist. Typically an orthopaedic surgeon can help you. If you are looking for specific sports expertise a sports medicine fellowship trained orthopaedist would be your best bet.
Sports surgery. To insure the best possible results one should find an orthopaedic surgeon with a sports certificate of added qualification. This means they've had a fellowship or have worked in sports medicine enough to qualify for a difficult test. It also helps to find a sports doctor who specializes in the problem you need fixed. Usually this breaks out to shoulder docs, knee docs and hip docs.
Orthopaedic . Orthopaedic surgeons all get training in the treatment of sports-related musculoskeletal injuries during their residency years. Some go on to specialize in the treatment of these injuries by doing a fellowship in sports medicine. In this training, they learn more about specialized surgical techniques to treat injuries commonly seen in the athletic activities. Depending on what your injury is, a general practice orthopaedic surgeon or a sports fellowship trained orthopaedic surgeon will be able to help you.