But MacPing sounds promising too! Never heard of it, but will give it a gander.

EDIT:

That would indeed do the trick, it seems from the manual, p. 28. You just write in the custom packet and direct it to the subnet/broadcast address of your router, or indeed send it out on ethertalk as Gorgonops explains. The application is also scriptable, so it could be called from a System 7-9 webserver through an AppleScript CGI.

I am kind of pumped about the Newton option, but if my Newton idea does not work, I'll know where to turn next.