Can you change an MOV to an MP4 without transcoding?
Solution 1:
You could do that with ffmpeg:
ffmpeg -i video.mov -vcodec copy -acodec copy video.mp4
This will just change containers, but obviously will only work with a codec that ffmpeg supports.
Edit: if you absolutely need a GUI, you could use Automator to create a Drag & Drop target, like this: