video – FFMPEG Applying Mux Operation to All Files in Folder Structure

I have two identical folder structures containing video files (containing varying audio channels) – one has the originals, one has proxy (lower res) versions.
The process of making the proxies messed with the sample rate of the audio, so now I need to replace the audio from each proxy clip with the audio of the respective original clip.

It seems like that is something I can do with ffmpeg without transcoding all of the files again:

$ ffmpeg -i original_clip.mov -i proxy_clip.mov -c copy -map 0:0 -map 1:1 proxy_new.mov

The issue is I have no idea how to make this happen for all files in a folder structure, and with the output also ending up in an identical folder structure. Any help is really appreciated, this issue has caused quite a mess…