From a strict anatomical standpoint, it is probably fine to undergo Coolsculpting of the submental fat excess since it is distinct from the thyroid region. Of course, this assumes you have healed appropriately from the thyroid surgery. Consult a Coolsculpting specialist for specific advice.
Thank you for your question. The best way to maximize the benefits of CoolSculpting is to maintain a healthy diet and exercise regimen. There is evidence that any of the other methods you have mentions would help remove any extra fat. Please talk to your treating physician before taking any...
You need to be seen to determine which procedure is best for you. There have been great results with CoolSculpting around the armpit if your skin has good elasticity. Good luck.