Have you simply tried something like this (caution: works in recent Perl releases)?

#!/usr/bin/perl -T
use strict;
use warnings;
use CGI::Carp qw( fatalsToBrowser );
use CGI qw( :standard );
                                                                      
+          
# Try to open a simple, splendid filehandle
open my $fh, ">", "/delme/final_zipfile.zip"
   or die "open(): $!";
                                                                      
+          
# Print a greeting message
print header(), start_html("Opened successfully"),
   h1("Opened successfully"), end_html();
[download]

You'd be able to work out if Archive::Zip is the real cause of your troubles. If not, try to work around using writeToFileHandle while you dig the problem in depth.