How do I display a String as an HTTP hyperlink in a dialog box?
You should be able to create a subclass of java.awt.Canvas and then simulate the behavior of a Hyperlink yourself. Draw the link text and then an underline using the Graphics.drawString(...) and Graphics.drawLine(...) methods.
Also register a MouseListener to detect clicks over the hyperlink. Also register MouseMotionListener to track the mouse to show 'mouse-over-hyperlink' feedback.