They are the best qualified to deal with
ovarian cysts, even those that turn out to be benign. If you do end up having
surgery, have it done by a gyn. oncologist, or at least ensure that they are present at the surgery. In the unlikely event that it would be cancer, you definitely want a gyn. oncologist to be the one handling the staging during surgery.
Believe me, I know that staying calm and not thinking the worst is easier said than done.