Yes ssleay is the way to go. I would do something like this:
Compile openSSL
Compile ssleay
Then insert this code:
use Net::SSLeay qw(get_https make_form);
($return_code, $result, %headers) = get_https('secure.url.com', 443, '/path/to/cgi', '', make_form('name'=>"$value", 'name2'=>"$value2"));

$return code will be the result of the cgi you called to.

symŽ