Can you record video without the audio

There is no way to turn the audio off on the iPhone. You may use software to edit the movie afterwards to remove the existing audio and replace it with your own track. Pinnacle is an option I've used in the past with video, as well as Windows Movie Maker. I see you use a Mac, but that ability has to be there as well.

Edward,

I would like to record the audio separately as a commentary to the video.

That can easily be done with iMovie.

http://www.apple.com/ilife/tutorials/#imovie-voiceover

Matt