It depends if it's a voltage that's triggering the speaker via a circuit on that IC, or if it ends up powering the speaker directly, and I'd bet the former. Putting a resistor in series with one of the speaker leads is more likely to achieve what you're hoping for (without knowing more about the circuit).

Do voices and the buzzer sound come out of the same speaker shown in the picture, or is there a separate little "buzzer" speaker in there?