Thanks to a suggestion by Bart I have now met my requirements. The new code is

#!/usr/bin/perl -w
use strict;
use warnings;
use Archive::Zip qw( :ERROR_CODES );
my $zipfile = "/tmp/test.zip";
my $zip = Archive::Zip->new();
   unless ( $zip->read( "$zipfile" ) == AZ_OK ) {
       die 'read error';
   }
my @members = $zip->memberNames();
my $fileNames = join(', ', @members);
print"fileNames=$fileNames";
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