We do something similar to what you are describing: some mics are not in the main FoH mix but are used for our livestream mix (e.g. piano mics, room mics). What we do is set all channels to post-fader so that the faders affect both the FoH and Livestream mixes. But for the channels not used for FoH we don’t route them to the L/R mix. Now, changing fader position of those channels even when you are mixing L/R FoH will only change them on the Livestream mix and they won’t ever be present in your L/R mix.
With the L/R mix selected, hold down ASSIGN. The SEL button on each channel will light up if it is assigned to that mix. uncheck any channels you don’t going to FoH. (in manual sheet 42 that SQuser attached above)