Possible to Reduce the Size of an Adam's Apple?

Yes, this is a relatively quick surgery that can done under local anesthesia (don't have to go to sleep) through a small incision at the top of your neck.  To make sure it is as safe as possible I would use a small camera in your throat to watch your vocal cords through the surgery.  

Bryan Rolfes, MD

For more than 35 years I have done this procedure hundreds of times without any complication in both males, females and transgender patients. It is safe and the incision is placed in a crease above the Adam's apple. It can be done under local anesthesia without pain.

The adam's apple prominence can be reduced by shaving down the cartilage. Historically this was done via an incision in the skin right over the cartilage. It is now done via a longer but less visible skin incision higher up along the natural neck skin crease that is easily visible in the photo that you submitted. It is not a commonly performed procedure.