Oddly enough, zip files are a supported playlist format in VLC, so you can just have them open the zip file. I don't recommend it, but it's technically a solution.

Making an actual playlist and having them load that instead would work around your VLC problem and should work in other music players. An .m3u playlist is fairly well supported, and it's really just a list of file names in the order you want them played. Remember to use relative filenames so it works wherever the zip file is extracted.