My first thought for a compact, air-blower would be the inflater for air mattresses. They're already fairly small, have a high flow rate, and exist in forms which accept 12 VDC.
Another option is a small tank of compressed air, but that option is either heavy (steel tank) or stores air at inefficient, low pressures (plastic tank).
I suppose a third option is to rig a can of air-duster so that it blows through the whistle. That would be mechanically simple to implement a solenoid to press the valve, although there is a small environmental cost to using cans of air-duster regularly.