How to exclude an audio input from program mix only?

I have a question regarding separate audio mixes. Is there any way to bypass an audio input from a live broadcast and still use it in a custom audio mix?

I am trying to set up a separate audio mix that is sent via NDI output. In the audio mix I want to include sound from an input which in turn should be excluded from the “program mix”.

It seems that all audio inputs must first be fed through the “program mix” to be available in a new (custom) audio mix. If I understand correctly, then all audio inputs must be live in the broadcast to be used in separate audio mixes?

Alternatively, is it possible to assign a custom audio mix to the program output?