The easy way is to just pull all links and apply your regular expression outside:

...
my @outbound_links = grep { $_->url !~ qr!^https?://$hostname/! } $mec
+h->find_all_links;
...
[download]

The harder way is to make your regular expression look ahead and ensure that it doesn't match:

my @outbound_links = $mech->find_all_links(
    url_abs_regex => qr<^(?!https?://\Q$hostname\E/)>,
);
[download]