I literally just went through the doorbell issue yesterday after about 2 months of thinking/talking about it...
Here's the thing - the 930 is great for detecting the ringing of the doorbell with the existing doorbell still hooked up - but it doesn't interrupt the doorbell and in its native fashion, it keeps the doorbell light, still rings the doorbell, but allows you to also capture the doorbell to trigger automation by sending a pulse to a zone input. It won't function without the existing doorbell to trigger the current draw.
This thread talks about some of the options around all that:
http://www.cocoontech.com/index.php?showto...amp;hl=doorbell
I followed BSR's advice for a quick fix and stripped the doorbell apart so that it couldn't make the chime noise, but still drew enough current to trigger the 930. The way the 930 works is that when the doorbell that's connected in-line with it draws current (from activating the plunger) it does a pull-to-ground on the other zone-input circuit. If you didn't want to use the 930 and keep your doorbell (even dismantled and out of sight) you could use a 16VAC relay (hard to find - see my notes) and use the contact closure of the relay to also trigger a zone - but I couldn't get the right relay quickly.
For the purposes of muting the doorbell, your best bet is exactly as you confirmed back - use a relay that, when activated, disrupts the circuit. As you noticed, the added bonus is that the light goes out too (I didn't mention that, but thought it was a cool side effect).
Otherwise, you can completely eliminate the doorbell for the audio and have the trigger instead activate the playing of a sound - all through the HAI - in which case it's easy enough to add a rule that says "when input X is triggered AND the hours are between X and X, Trigger sound X". All of the different methods of eliminating the doorbell are discussed in the above thread.
Now - using the doorbell detector and the method above may not give desired results, as if the relay is disabling the doorbell, the pressing of the button won't trigger the 930 either. In that case, you'd want to get a little tricky with the wiring. If that time comes, post some details on here about exactly what you want, and we can point you in the right direction.
In my case, my ultimate goal is to completely eliminate the existing doorbell while keeping the light - so I'll be replacing the doorbell and the 930 with an appropriate 16VAC relay that, when triggered, closes the zone momentarily. That'll elminate the 930, allow the light to still work, and get rid of the existing doorbell altogether.