First of all, you can not do this just in Adobe AIR. So, a third-party tool is a good choice:
- Install 3rd party hotkey application (like AutoHotkey or HotKeyBind)
- Configure hotkey application to launch your AIR application.
- In your AIR application, register for the NativeApplication.invoke event, and watch for arguments to do something.
Maybe the Adobe AIR will add those features in the future.