My first thoughts are either a food grade drying oil like walnut oil, or homemade milk paint, both using finely powered charcoal as the pigment.

Walnut oil will polymerize and cure, so shouldn't continue offgassing to affect your food's flavor.  Use a fan to move plenty of air over it for a few days to speed oxidation and curing.

Milk paint is essentially just curds from nonfat milk blended up with pigment.  Curdle the milk using lime or lemon juice, strain out the curds, and then blend it up.  Add water to thin if, needed.  I'm not sure how milk paint will do in a humid environment like a dehydrator, so you may need to seal it, perhaps with a coat of walnut oil after it's fully dried. 

 Thanks for the detailed response. I think I will put a coat of oil on the egg and charcoal mix I used