Depending on the device you are able to obtain the actual fingerprint image and even receive events like finger placed or removed etc. The website that leveraged the device via the website, did that need some sort of plugin or ActiveX component? If so, it hard to recreate without such broker layer in between.
The best thing would be to disrupt the distribution of your AIR application in such manner that you install the framework and then just deliver the application yourselves in combination with a launcher app which will start the broker and after that the actual AIR application. In an upcoming book about Adobe AIR this is shown and leverages Java (wide audience) and currently working on a second example whereby we will probably leverage RFID readers. Maybe an fingerprint reader would be an interesting topic too. Shouldn't be a lot of work.

