As most mice nowadays to a large degree are shaped ergonomically, with rounded edges, easily accessible buttons/scroll wheel, and shaped for a cupped hand, only a few designs are specialized.
Different sized mice are available on the market.
Roller/Track ball designs are basically the older designed mice but inverted, instead of moving the mouse body (it remains fixed) the fingers (and thumb) rotate the ball. This can be helpful for those with little desk space or lacking a smooth surface, and helps with precision. This may be helpful for individuals with sore wrists. Shown: Logitech® Wireless Trackball
M570 and Trackman Marble
Upright mice may be beneficial for those with wrist problems (especially with carpel tunnel syndrome). This mouse helps limit pressure on the underside of the wrist by reducing compression of the structures in that area.
Touch pads, similar to those on laptop computers are now available separately. They work in the same fashion where the finger glides on the surface and moves the cursor. Intuitive hand ‘gestures’ click, scroll, swipe and perform a variety of other functions without the need for buttons. Shown: Apple® Magic Trackpad.