Generally the hardware layer does not matter much to Java (the degree of abstraction is such as the strength and weakness of Java), so according to me the best way would be an application that shows what you want to show in full screen and leave the way the OS connects with the device to the OS.
To go through the available screens (in the case that you have a screen connected to the hdmi) you should serve:
GraphicsEnvironment ge = GraphicsEnvironment.getLocalGraphicsEnvironment();
GraphicsDevice[] gs = ge.getScreenDevices();
Then to put the device of your choice in full screen mode you can use the exclusive mode :
GraphicsDevice miDispositivo=gs[miSeleccion];
Window miVentana;
try {
miDispositivo.setFullScreenWindow(miVentana);
...
} finally {
miDispositivo.setFullScreenWindow(null);
}