This is possible. In Settings->Output, for streaming, you can select one track that goes out with streaming, and for recording, you can select different track(s) that are written to a recording. Choose one track for streaming and a different one for recording. Open the advanced audio properties by right-clicking any of the audio meters, then for the streaming audio track check all the audio sources that should go out for streaming and do the same for the audio track that is written to your recording but leave out the desktop audio souce.