I'd recommend more defensive programming, as follows:

  my $zip = Archive::Zip->new()
    or croak "Failed to create a new archive";

  $zip->addFile($renamed_file)->desiredCompressionLevel(0)
    or croak "Failed to add $renamed_file) to archive";

  if( $zip->writeToFileNamed($zip_filename) != AZ_OK ) {
    croak "Failed to write to archive: $!";
  }
  print "Added $renamed_file to $zip_filename\n";
[download]

I've merely copied your use of $! in the last croak; I'm not sure if that ever gets populated by Archive::Zip.