Thew purpose of Ammonium Hydroxide is to dissolve what ever minute amounts of Silver Chloride is left, it will also dissolve Copper if it is there and the blue color is a clear indication.Would you recommend washing in nitric for greater purity? I was only planning to wash in water and HCl, many times of course. I've heard some, Harold and others recommend ammonium hydroxide too.
And no, there is no reason to use Nitric, at least not if you can't get it cheaper than HCl.