I have a 4cm cyst in my throat above sternum, its pushing against my thyroid, larynx and esophagus. what are the best surgical practices and risk invo?

Thyroid cyst: If it is a thyroid cyst, and there are no worrisome features on ultrasound, then it may not require any treatment. Unless it causes trouble with swallowing or breathing. Important to find a surgeon who does a lot of thyroid surgery. The surgery is usually straightforward, often outpatient. Risks are to parathyroids and nerve to larynx, but risk is low in good hands.

See an ENT doctor: You should see an ENT (ear nose throat) doctor. They are formally known as otolarygologist. They are surgeons who can best advise you. It sounds like you've had an initial work-up. Are you seeing a surgeon or do you need help finding one?

See a surgeon: You need to see a doctor that can do a full evaluation to get a diagnosis. There are many things that could be causing that mass. Some of those things are benign and some could be more serious. Since surgery is a likely treatment you should start with a thoracic or ENT surgeon.

Need more work up.: This could be many things. If you can see this mass for the outside, it would likely be a superficial cyst, thyroid mass, possible a thyroglossal duct cyst if midline. If the mass you are describing is seen inside it could be a cyst, carcinoma, lymphoma. You need an exam, poss. Endoscopy, poss. Ct imaging, poss. A biopsy. I can't stress enough to see an experienced ENT or head ; neck surgeon.