I have been using zappers for 15 years. I also design, produce and market them.
I have never nursed a child so that is one thing that I can not answer. I will say that it is important not to zap at the same time that you are nursing as it may have some effect on the infant which is obviously too young to tell you of any problems that it may experience.
Otherwise, I would certainly wash my hands after zapping and before handling any child. This should be a given.