Hi,
What you're suggesting is feasible, but rather than a voltage regulator you'll probably want a voltage divider sized to suit the maximum voltage you measure during a chirp. A voltage regulator will shape a voltage higher than 5V down to 5V but a divider constructed from a pair of resistors will be cheaper. Then teach your Uno to look for the voltage changes, likely using an interrupt on an input pin. You might also look to the confirmation that flashes the indicators/hazards on the car since at least you know that should be a 12V trigger that you can voltage divide down to 5V for the Uno input quite simply. Or maybe tap into the line that runs to the flashing LED on the dash? Lots of options 
You might want to check how loud that shield is first though, depending where you're mounting this.
Cheers ! Geoff