It was easy when I did it...

First, I deliberately set off the buzzer a few times so that I could triangulate approximately where inside the body of the machine it was located.

Then I set upon the machine with a screwdriver and other tools, dismantling it until I could reach the buzzer. When I finally reached it, it was easy to disconnect. Electrical tape over the ends of the wires to which it used to connect, re-assemble the machine, and all was right with the blissfully silent world.