If you want compatibility with modern QuickTime, it's probably the best idea to convert the files. You should keep the originals if disk space allows so that, if you ever need to convert them again, you can again use the original files and don't go through lossy re-encoding too often. A good tool for encoding video files is ffmpeg.
Are they all the same kind of codec and container format? Can you post the output of ffprobe for one of the files here? Then someone can give you more concrete advice how they should be best encoded. For example, if it's just the container format that became incompatible, then maybe the video/audio streams can even be just copied.