I don't see this being a problem directly. You will have some advantage in the way of citations and links to
www.website.com/PublishersPage from the affiliate websites, but then these links will then redirect to the script via .htaccess and then back to your website.
How many affiliates are we talking ? If you think from the affiliate perspective, they'd like it as well I am guessing because if I am the affiliate, I would love to link to www.website.com/PublishersPage vs http://scripts.affiliateprogramme....../..../....)
Do yes, definitely consider doing it. Your affiliates are going to love it. I don't see a lot of merchants doing this. This is definitely something unique.