# in wrapper . . .
use Fcntl qw( F_GETFD F_SETFD FD_CLOEXEC );
open( LOG, "/path/to/log" ) or die "open log: $!\n";
$ENV{LOG_FD} = fileno( LOG );

my $flags = fcntl( LOG, F_GETFD ) or warn "getfd: $!\n";
fcntl( LOG, F_SETFD, $flags & ~FD_CLOEXEC ) or warn "setfd: $!\n";

$< = $> = uid_to_run_as( ... );
exec "/path/to/real/program", @prog_args
  or die "Can't exec real program: $!\n";

# in your module
sub log_it {
  local( *LOG );
  open( LOG, "<&=" . $ENV{LOG_FD} ) or die "Can't dup log fd: $!\n";

  print LOG, "Ack: ", @_, "\n";
}