If you did put the audio into the laptop as a FILE/wav or mp3, then you could process the audio >> clean/edit/ compress, using an audio software. But then you would have to sync it back up with the video.
If you send it straight to Movie Maker as a source, its basically the same thing you’re doing now.
You can get adapters to go from your mixer to the laptop line in. You could produce a bit of a stereo field if that mixer has a l/r balance and you’re using several mics.
Sounds like your end use is simple, so therefore I would recommend that you keep the entire setup simple. Stick with the way you’re doing it.
