Can’t be done. A Shotcut export is always an encoding task, not a codec copy task.
However, you’re familiar with ffmpeg, so there is an alternative.
Bring the video into Shotcut. Edit your audio as you intended. Export the audio from Shotcut. (There are audio-only presets, or you can cook your own.) Then we can effectively swap audio tracks with ffmpeg:
ffmpeg -i Original.mp4 -i AudioOnly.aac -map 0:V -map 1:a -codec copy AudioSwap.mp4