Because polarization changes with angle of incidence and reflection you won't be able to kill all reflections on all areas of a sphere.

A reflective sphere is going to reflect the environment around it, so your best bet is to create a uniform environment. For this image of my wife's eye I used a long white sock with the foot cut off. She held one end open around her eye and at the other end was the lens. The lens will make a dark circular reflection; care was taken to place it over the pupil (which was edited out/replaced). The farther away the lens is, the smaller its' reflection.

This is basically the same as using a diffusion dome/cone which can be purchased commercially. Or here's a couple of inexpensive DIY options... one is a dollar store bin with a hole drilled in it, the other is a white lamp shade. Keep in mind that the size/location of the opening will determine the size/location of the dark reflection spot if it is larger than the lens itself. Also note that DIY solutions are unlikely to generate entirely accurate colors (not that commercial versions necessarily will).