As I understand it, any alteration of the surface patina, no matter how unsightly it is, will damage the value of the coin. But to summarize your chemical choices: Ammonia will only slowly remove the silver compounds. Chemically, I don't believe ammonia will attack coinage silver, so right away, we came face to face with the fact that removing the patina is bad for the coin regardless of method. I don't know about sodium thiosulfate, I've used similar things, like Tarn-X on silverware, but its probably too harsh for your coin. I don't understand how silver nitrate will help with tarnish on silver, except to function as a weak acid to dissolve the tarnish. The method you seem to have been given only part of -- the zinc powder/iron nails solution is so called electrolytic tarnish removal -- basically you put a tarnished silver article into a pan of hot sodium carbonate/sodium chloride solution with a piece of aluminum foil, and the tarnish transfers to the aluminum.
Just remember, and don't kid yourself, all of these methods strip some silver off the surface. The removed tarnish takes some silver with it. There's no way to reverse the tarnish process and get the silver metal to redeposit in a even surface equivalent to when the blank was stamped by the die.