mifflin gives you the correct solution for calling the external utility (though I'd just test for false or $@ instead of zero).

If you are on a system where .zip is the usual archive format you ought to have Archive::Zip available. That will make your choice of files to include in the package much more flexible.

I don't like your use of relative paths for this. You don't know that the http server will make the cgi directory current for a run. If some DirectoryIndex points to your script it will run in that directory, instead.