The only thing you can do is:
- not use Starling (transparency is not supported, see below..)
- set the AIR application to "transparent" (application descriptor, <transparent>true</transparent> + <systemChrome>none</systemChrome>),
- add a Sprite with BlendMode.ERASE on stage
- manually position the external window at the position of the cut out sprite/rectangle
This also means you need to react on native windows move and resize events and update the external windows position on each change.
You will need to create a communication gateway/interface (e.g. using UDP sockets or some kind of REST interface on localhost) between your AIR app and the external app for this.
Its quite some effort but when you succeed it will be possible to have any sort of AIR (G)UI displayed above your external app. The transparent/cut out area will let mouse events pass through so you can even control the underlaying application. EDIT: Interaction can of course be blocked with a transparent mouse event receiver/interceptor (e.g. something like an interactive Sprite)