Will jaw surgery fix my double chin? (Photos)

My orthodontist says I am elgible for jaw surgery because I am a class 3 malocclusion (small maxilla) and I have mild sleep apnea. My functional symptoms are very mild so I am looking into jaw surgery for aesthetics. My main concern is the fat under my neck and my small chin. Will jaw surgery fix those or would I be better off with a genioplasty. I am worried advancemnt of my maxilla or mandible will leave me looking like a chimp because of my flat midface. Is my hyoid bone too low?