From the LWP documentation :

The libwww-perl response object has the class name
       `HTTP::Response'.  The main attributes of objects of this
       class are:

       ·  The code is a numerical value that indicates the
          overall outcome of the request.

so, what you want to do is change

if(($ua->request(HTTP::Request->new('HEAD', $url)))->is_success())
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and following lines to :

my $response = $ua->request(HTTP::Request->new('HEAD', $url));
if ($response->code == 200) {
    # url is valid
} else {
    # there's something odd with the URL
}
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Philosophy can be made out of anything. Or less -- Jerry A. Fodor