You don't really need a trusted host relationship, you just need passwordless keys. If passwordless keys are impossible, then you will have to use the interactive method. Maybe you can go forward by hacking Net::Ssh::Perl to redirect the STDOUT part of the connection. Looking into the source of Net::SSH::Perl::SSH1, there seem to be handlers like SSH_SMSG_STDOUT_DATA and replacing the default handler with something that doesn't accumulate the string might help:

# 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 });
    }
    ...
}
[download]

I would try to supply my own callback like this:

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]; });
[download]