Is it okay to eat with my hands even though they're stained with silver nitrate?

The silver ion is very easily displaced from the nitrate ion, making it corrosive by liberation of NO2, the silver metal when in contact with your skin will turn it black also upon exposure to UV light (ordinary daylight is enough), although it`s not in itself toxic per se, there is a condition called Argeria in which the person exposed to excess silver will actualy turn Grey!

a corroding iron, if that's one of your choices