MPEG Streamclip from Squared 5 will do the job for you -- but only if the audio and video is not copy protected with DRM. Here's how you do it.
From iTunes, right-click (Control-click) your video and select Show in Finder.
Drag that file into MPEG Streamclip.
Make sure the video can be played back by scanning along the scrubber bar. If it can't, you're out of luck.
Choose File > Export Audio....
Select your format (MP4 AAC is what you want), leave the channels as Stereo, the sample rate as Auto, and the bit rate at 256 kbps.
Select where to save the new file and click Save.
Once converted, you can drag the newly saved file into iTunes, add it to your favorite playlist and sync it over without wasting so much space on your device.
One final note, if you like the music that much, the artist would probably like it if you said thanks by buying his newest album when it comes out, apparently later this year.
P.S. For those who are wondering (Auntie surely did), he's 19. Looks 13. Sorry, Jenny, this postscript is for us crusty older folk. Auntie will stop now and hide.