Mine didn't have a buzzer at all. Didn't like that. especially since the little red LED that lights up is impossible to see during the day, even if you're looking right at it - a task that requires my bending down to look, since the panel is on the side of the cockpit.
Anyway, I put in an obnoxious little siren from Radio Shack, and connected it in parallel to the same circuit as the LED. Works fabulous. I wanted a hideous alarm, for I want to hear it and know what it is if it trips, no matter what other noise is occuring. It's actually inside the lazerette on the bulkhead, so it had to be extra loud.
To answer your question, I also installed a marine toggle switch in the same circuit and mounted it right next to the siren. With this setup, if I'm in a quiet anchorage leaving out early, I can start the motor, then flip the switch back on for safety. A switch might work for your issue too. They're dead easy to istall; you just need to get behind the panel.