Affiliates can't do this themselves, only a merchant can change the way the url is displayed on their page (they can add a script to their page to do this).
However, what you could do is either cookie stuff all your visitors and send them to the merchants page directly or send them to a page like
http://yoursite.com/1.html and cookie stuff them on that page with an auto redirect. That way you're not really doing anything wrong as you're just hiding your aff id and not cookie stuffing every Dick and Jane.