You can use ffmpeg to copy the tracks from mov to mp4 files. See Example 9 on this FFMPEG wiki page.
If you’re good with scripting (which I’m not), you could write a short script to process all the files in a given directory.
I’m not sure how much metadata is copied over, so it may be best to convert before adding a lot of info to a movie.
I ran a test on an old video shot with an iPhone 3GS. It copied the video & audio tracks from the .mov file to a .mp4 file. The tracks are copied, not transcoded, so the output file is roughly the same size as the input file.
c:\Temp>ffmpeg -i test.mov -map 0 -c copy test.mp4
Steps:
Download ffmpeg from https://ffmpeg.zeranoe.com/builds/. Version 4.2.2, Win64, static libraries.
Put ffmpeg.exe and test.mov in c:\temp
ran the command from a c:\ prompt.