Would a chin implant / genioplasty help slim my face or should I consider a cheek lift? (photo)

I’ve got flat cheekbones and a weak chin which means any tissue, fat etc migrates down my face. This has led to my lower face looking rounded in appearance, with no real jawline definition. So my questions is, would a chin implant or genioplasty alone have any slimming affect on my lower face, via stretching out the existing migration of tissue, fat etc? Or would a cheek lift be a better way of doing this, dragging the tissue, fat etc back up for face?