Yes, that's possible. In Settings → Output, no matter if simple or advanced mode, you're able to select which audio track(s) will go out to the recording. For streaming, it's track 1 that's going out as default (changeable in advanced mode, but you're supposed to leave it at track 1).
To have a different audio source composition for recording, select a different track for recording, for example track 2. So you output track 1 for streaming and track 2 for recording.
Additionally, define which audio source is mixed to which track. For this, open Edit → Advanced Audio properties and in the "Track" matrix and select/unselect corresponding sources. You will probably unselect the mic source for track 2 to avoid your mic mixed to your recording.
