Normally, you shouldn't need to worry about extracting or setting the cookie at all. If $RevAddr sends a cookie it will be in cookie jar, and it will be returned automatically:

my $ua = LWP::UserAgent->new;
$ua->cookie_jar( {} ); # auto calls HTTP::Cookies->new
my $response = $ua->get( $RevAddr );
$ua->timeout( 10 );
$ua->show_progress ( 1 );
$response = $ua->get( $ClickHere, ':content_file' => './eraseme.bin' )
+;
[download]

However in this case the cookie is set by a javascript function, so the above will not work. But as you already know the cookie you can set it directly:

my $ua = LWP::UserAgent->new;
$ua->timeout( 10 );
$ua->show_progress ( 1 );
my $response = $ua->get(
    $ClickHere,
    ':content_file' => './eraseme.bin',
    'Cookie'        => 'oraclelicense=accept-securebackup-cookie',
);
[download]