Hmm...what's this Wii Cord-Free adapter you speak of?
EDIT:
Nevermind I googled haha.
ZOMG. It's cool. It would probably piss me off though...
Yeah, it'll work on the controller [at least, it SHOULD work] but your just gonna have to plug it in, so that the adapter is like...just hanging down. So essentially it'll be just as bad as having it connected to the wiimote. Lawl.
You could try
THIS instead though