for my $file_name (
   keys %{
      $hash_name eq 'dat'
         ? \%dat_mapping
         : \%eng_mapping
   }
) {
    ...
}

##</code><code>##

my $hash = $hash_name eq 'dat'
   ? \%dat_mapping
   : \%eng_mapping;
for my $file_name (keys %$hash) {
    ...
}