Try "SkipBad" from Net::SMTP. I would try it like this:

#!/usr/bin/perl

use strict;
use warnings;
use MIME::Lite;

my $msg = MIME::Lite->new('your stuff here');

MIME::Lite->send(
                'smtp',
                'localhost',
                Debug    => 1,
                SkipBad  => 1
);
$msg->print(\*STDOUT);
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