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.

You could base your design off my favorite bike accessory, the Airzound bike horn

Install it with the mouthpiece facing the wind

I work in industrial automation and have a background in pneumatics. I think you'll be surprised at how inefficient pressurizing/moving air is. I think the most practical solution (if you can call it that) is likely carrying an air reservoir that can be pumped up with a bike pump, and having a valve to trigger the whistle. There isn't really a safe way to carry compressed air on a bicycle because it's inherently dangerous to transport. There are lots of ways to make an unsafe air reservoir for example what Chris Notap on you tube does.