Looking for a material that is easy to manufacture, with no toxicity that can be used to create low profile palm rests, and where would I be able to get a prototype custom mold of it?

Silicone, generally. Talk to a podiatrist office about the shoe insert pads they sell.
Or take apart one of the many gel palm rests on the market already, or a Dr. Scholl's pad from a drugstore or shoe store. Or cushions for the paralyzed.

Where to have it made? I don't know.
I'd find out who makes the ones already on the market.