Record the Siri beep, put it in an MP3 player app and turn Siri off? Whenever you need the beep press play in the app, or hit the play button on the earphones.
Not likely a feature that a normal user would have much use of. Apple doesn't have options for even more straightforward and more useful features, so it's not surprising that a feature like this wouldn't be there. Not that I can really think of any manufacturer really offering something like that.
I don't understand why you can't just use this: Siri Sound... No one needs to have all the mics turned off, they are one of the main methods for input into the device, and would be near useless a feature.