I'd try the following:

use IPC::Run qw( run new_chunker );

sub new_prefixer {
   my ($prefix) = @_;
   return sub {
      my ($in_ref, $out_ref) = @_;
      return input_avail && do {
         $$out_ref = join('', $$out_ref, $prefix, $$in_ref);
         $$in_ref = '';
         1
      };
   }
}

sub new_printer {
   my ($fh) = @_;
   return sub {
      print $fh ($_[0]);
   }
}

{
   my @cmd = ('find', '/fst/home/', '-name', '*ooo*');

   open(my $fh_log, '>>', 'h1.log')
      or die("Unable to open log file: $!\n");

   my $printer = new_printer($fh_log);

   run \@cmd,
      '>', \$fh_log,
      '2>', new_chunker(), new_prefixer('STDERR: '), $printer;
      or die("Error executing child. Child returned $&\n");

   # or:
   #
   # run \@cmd,
   #    '>',  new_chunker(), new_prefixer('STDOUT: '), $printer,
   #    '2>', new_chunker(), new_prefixer('STDERR: '), $printer;
   #    or die("Error executing child. Child returned $&\n");
}
[download]

Notes:

• Untested.

• The above won't work (loss of sync between STDOUT and STDERR) if your application buffers STDOUT. You could try to get around that by changing '>' to '>pty>'. Read these notes for details.

• May not work on Windows due to inability to select file handles. Windows might also be unable to create PTTYs.

• new_chunker() assures that the prefix is added to every line.

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