you don't really need to use "visitorId" if you can't capture it on the 3rd party site. You can use only the "AffiliateID" for example. The whole point is to let the software know under which affiliate it should save the commission. "visitorId" is the best option since it contains all the click information like the banner which was used, campaign, when the click was made, also information about first and last click and so on.
or if you wish to append the cookie value to some a href link then you can use instead this method:
Example of how that works can be seen on http://demo.postaffiliatepro.com/samples_tests/cookie_info.php
where the Full cookie field is populated with the cookie ID which is basically the "visitorId" which can be used in the hidden pixel URL as a parameter.