"to input the sound from the mixing board directly into the camera"

If the camera has a mic socket, you need a cable with the right plugs on the ends and an attenuator to lower the levels out of the mixer down to microphone levels. A box with, essentially, four resistors in it (if it's stereo) is all. Much simpler than a radio link, unless there's a physical problem with running a cable between the desk and the camera.

I'd have though that the editing software (I don't know movie maker) should make it easy to sync the sound to the video anyway.

Anahata