maybe it would work, but I heard from good sources that genetics decide where to take fat from. It goes to the liver, is processed, and enters the blood when levels are depeated from muslces taking stuff out of the blood. The big muscles get rid of most of the fat. Doing crunches will not give you a 6 pack unless you burn the fat off with your big muscles.
Fat face may be genetic, or may mean you need to make your body more lean to finally tap your face fat. But smoking and drinking can do it too, and I think it is permanent. Smoking makes it happen much faster.
Even if moving your joy did burn local fat, your jaw just can't burn enough calories to do much. Sorry. You will be doing a lot of face exercises. Try not to get motion wrinkles.
I wish I knew of a cure. I know some inshape people who need it, and never smoked. Sad. I'm glad my face looks nice.
I know of people who had moderate body fat, and when they got in shape and put on lean muscle, the fat face disappeared, and their face went up 3-4 points on a 10 point scale. Amazing. Never thought that would happen. I think maybe mine can look better too.
So if your body is a bit lazy, even if not overweight, then fix that first before you dispare. And stop smoking if you currently do.