To avoid meat sticking to your hands, try greasing your hands with olive oil. The oil will make them more nonstick and will actually help crisp the meatballs up while they cook.
If you want to avoid touching the meat mixture with your hands, try using an ice cream scoop. The balls might not be perfectly shaped, but it will help keep them all the same size.
If you really want a sphere-shaped meatball, you can take a little plastic wrap, put it over top of the meatball, then shape it with your hands once it's on the sheet.