Handbrake gets my vote if you really want to convert them, but you might be better off using a different player, assuming you're just trying to use Sierra's built-in QuickTime Player.
VLC or
mpv (
mac download) can play pretty much any format from the last ~15 years. I also am locked to 10.12 Sierra on my old Hackintosh, and those two apps continue to work wonders for me.
If you can open one of these videos in VLC or mpv, take a look at the codec info they may provide for one of the videos. In VLC, press cmd-i and check the Codec Details. In mpv, press i and look under Video. A video I recorded from my old iPhone 6s running iOS 13.6.1 appears to have encoded with "H264 - MPEG-4 AVC (part 10) (avc1)" according to VLC (basically the same in mpv). That should be a pretty future-proof format.
Does yours show something different? If it mentions anything with "H265" or "HEVC", which might be the case for video recorded from newer iPhones, you probably
don't want to transcode the files again with Handbrake unless you
really need to use them with QuickTime Player or other older software. HEVC/H265 is the next major iteration after MP4/H264 that offers better compression and reduced file size. It should also be a pretty future-proof format, and plenty of open-source libraries and players have implemented it too (despite likely being very patent-encumbered).