There are probably a bunch of modules out there that would work. One of the most "zero setup" with which I have hands on experience is:
http://vorpalrobotics.com/wiki/index.php?title=Vorpal_Factory_Paired_Bluetooth_Modules
Pre-Paired at 38.400 baud (so change your Panel via the setup tab, and your printer via M575).
I believe that the BT module positioned at the printer would work from the PanelDue connector on the printer, with appropriate cable. The module on the PanelDue would also work, but SOMETHING has to provide 5V regulated power to both the BT module and the PanelDue.
I can see a million reasons NOT to do this… already mentioned above... however, if you do wish to pursue it, the above BT modules should be easy to try.