The file chooser wasn't designed to be customized in this way. The proper solution would be to customize the UI of the file chooser.
For a hack you can try using Darryl's Swing Utils class. The example shows you can access the text field. Once you have the text field you could add a DocumentFilter to prevent the document from being updated. Or you could change the font color to white so you don't see the text.
The code to access the label would be similar. Just find the label containing the text you want to change.