Jon Snow must be declared as an attacker (the normal way) in order to use stealth (gained from Master Luwin, etc.). If he participates in a challenge via his ability, then he was not declared as an attacker, and thus cannot use stealth.
Furthermore, if another Night's Watch character you control is attacking, Jon Snow is automatically in the challenge -- whether you want him to be or not.
The defending player cannot attempt to remove a Jon Snow that is participating, via his ability, from the challenge, because the ability will instantly reassert itself. They can, however, remove the other attacking Night's Watch character(s), and if there is no longer another attacking NW character then Jon Snow will stop participating as well.