how to obtain mouse click coordinates outside my window in Java

It is possible though limited:

Add an AWTEventListener for focus events. As long as your app has focus before the button is clicked you’ll receive a focus lost event. Then query for the pointer position.

The limitation is that, of course, your app loses focus. So depending on what you are ultimately trying to achieve this might not be useful.

If you don’t want to lose focus then you will have to temporarily take a screenshot of the whole screen and display that in a screen filling window which listens for a mouse click as usual.

Proof of first method:

import java.awt.AWTEvent;
import java.awt.MouseInfo;
import java.awt.Toolkit;
import java.awt.event.AWTEventListener;

import javax.swing.JFrame;

public class Application1 {
    public static void main(String[] args) {
        Toolkit.getDefaultToolkit().addAWTEventListener(
          new Listener(), AWTEvent.MOUSE_EVENT_MASK | AWTEvent.FOCUS_EVENT_MASK);
        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setVisible(true);
    }

    private static class Listener implements AWTEventListener {
        public void eventDispatched(AWTEvent event) {
            System.out.print(MouseInfo.getPointerInfo().getLocation() + " | ");
            System.out.println(event);
        }
    }
}

Clicking outside of the app produced:

java.awt.Point[x=198,y=59] | java.awt.event.MouseEvent[MOUSE_EXITED, ...
java.awt.Point[x=976,y=503] | java.awt.FocusEvent[FOCUS_LOST, ...

The second point is outside of the app.