I was mulling over this today during an idle moment.
If Lee was willing, how about a physical push "hush" button that goes into one of the PAW USB ports? So you push the button and the PAW either mutes, or swaps the verbal alert for a beep, for a settable period of time in the PAW software? It could appear to the PAW as a HID or serial input. It could be a panel mounted button, small button on a yoke, or perhaps any momentary button of your choosing (ideally momentary, doesn't matter is NO or NC). Could even light up when muted, and you could push it again to un-mute before the settable period times out.
Would be fairly trivial to sort something like that out pretty quickly, but only if Lee saw it as worth his time?