# Original code
sub cmd {
    ...
    unless ($ssh->handler_for(SSH_SMSG_STDOUT_DATA)) {
        $ssh->register_handler(SSH_SMSG_STDOUT_DATA,
            sub { $ssh->{_cmd_stdout} .= $_[1]->get_str });
    }
    ...
}

##</code><code>##

my $ssh = Net::SSH::Perl->new(...);
open my $outfh, ">", $filename
  or die "Couldn't create '$filename' : $!";
binmode $outfh;
$ssh->register_handler('stdout', sub { print $outfh $_[1]; });