Navigator proposes (to the one that discovered the hidden menu ;-) ) : Mute/Unmute.
Waze proposes : Mute/Alert Only/Unmute
I would suggest you a 4th mode : Quiet.
Mute: Just mute all TTS/annoncements/alerts
Alert Only: Mute TTS/announcements but play alerts like:
Speed camera
Speed limit reached
Recalculating route (due to the user not following the computed route)
Recalculating route (due to traffic ahead)
Quiet: Same as Verbose but where any direction TTS is replaced by a beep (not too loud please). This is nice when you mute it because you know the way but still want to be aware of the direction changes (because, the routing might be different than usual due to unusual traffic ahead). This is nice as well when children are (finally) sleeping ;-)