Whilst buffering the file open Audacity. Go to Edit > Preferences > Recording > Device > Stereo Mix. (Vista/Win7 may need some tweaks in control panel's sound settings.)
When you are ready hit record and start the play back of the streamed file. Once the file has finished playing hit stop, you can now highlight and delete any empty space. (If you are an IE user you won't be able to surf as the 'clicking' will be recorded too.)