You can record the audio separately from the video in My Screen Recorder.

To do this, click on Tools >> Settings >> Recording. De-select the check box for 'Record Video' and My Screen Recorder Pro will create an audio only recording.

If you want to record both audio and video and then separate it into two files, one with video and one with audio, you can use Digital Media Converter Pro. Add your recording to Digital Media Converter Pro and convert it to MP3 to get an audio-only file. Add the original recording again and select the Effects button, then reduce the volume to 0 and convert to any video format to get a video-only file.