Insofar as no property rights are violated in the process of gathering information about someone and publishing them somewhere, then there is no NAP violation and doxing per se does not violate the NAP. As Rothbard and Block pointed out, (there is no such thing as a right to privacy)[https://www.lewrockwell.com/2013/07/walter-e-block/there-is-no-right-to-privacy/].

Now, clearly rape does violate the NAP since it involves the initiation of force. However, self-harm does not violate the NAP, since you cannot initiate force against yourself; otherwise anybody that has committed suicide is a murderer.

So this means that telling someone to commit an act of self-harm in order to prevent you from publishing their dox is not a NAP violation - obviously assuming that no property rights have been violated in the process. Obviously it is a shitty thing to do to someone, but as Block pointed out, (blackmailing someone does not necessarily violate the NAP)[https://mises.org/library/defending-blackmailer].