I don't know if the mute wire was a ground wire or a hot wire.
I answered your question. Since the Nokia interfaced ok with the Becker (ie muted the radio when the phone was active), it had to be ground when active. That's because the Becker needed a "ground" to mute. Is that clearer?
For the Nak, your relay idea using the Nokia's mute line to provide ground to energize the relay, thereby removing power from the Nak. Do this by wiring the Nak's power through the normally closed
contacts of the relay. Understand?