The Mix Dial dictates what is hear from the Headphone Output, Main Outs and the Cue outs.
This should not effect what is recorded/analyzed in software. You can turn the Mix Dial all the way to the RIGHT to Playback. Then mute input audio or turn OFF input monitoring in Sonar.
I can't speak to the analysis software you mentioned, but if it works as a insert or plugin effect, you should be able to do the above without feedback.
Additionally, you assign the Sonarworks sweep sound to OutPut channels 3 and 4. This way you can set the Mix Dial to whatever and record to any input. However, you may still need to disable input/direct monitoring in Sonar to avoid feedback.