You have to re-zip the files, of course - but it's not so simple as that

The mimetype file must be first, and it must be uncompressed. With Linux, I use a two step process:
zip book-file.epub -DX0 mimetype
zip book-file.epub -rDX9 *
Linux zip does not require the .zip extension, and I'm obviously using the command line. For the Mac, pdurrant has written a script that does all the right stuff. I'm not sure how the Windows version of zip differs from the Linux version. Perhaps someone else can jump in on that aspect.