If you don't want to wear a wig then this synthetic hairpiece for the hair loss headband is a fantastic option. It's extremely light so you can't feel you're wearing anything.
It's large enough to fully cover the back of your head. When worn in combination with the headband no one will see any patchy or thin areas of hair. You could also add a fringe in a matching colour.
Tie your hair into a high ponytail and attach the piece using the combs and grips if necessary. If you don't have any hair then simply stitch it to the headband.
Synthetic hair is a fantastic choice for exercise as it washes easily in cool water, isn't effected by chlorine or colour fade. It looks totally natural both wet and dry.