<p>(y/N)</p>

<p>Edit: Read-only access is fine.</p>

If your willing to force the user to also install another application, you could write a small C# or C++ windows service that simply opens a Socket that provides some kind of protocol for accessing the registry. Then in AIR you can use the Socket class to send messages to/from the C# service that would return results to the AIR app.
When the app loads you can try to connect to the Socket, and if the connection is rejected you could prompt the user to download/install the service.
As for direct access to the registry I am pretty sure Adobe wouldn't allow that from AIR.