"quick & Dirty":That is "quick and dirty" for someone that knows nothing about electronics??? Really??
In continuation of post #10 which I think only 1 person saw..
Tape one of these over the speaker. It will quiet the speaker considerably, and possibly make it totally inaudible.
https://www.sparkfun.com/products/12642
You can interface with it via an Arduino, from another room.
There is no need to hack into the device and modify any wiring whatsoever.