Why on earth would that be impossible? There are so many ways I used to do that. For instance:
iframe the vendorspage (using your hoplink) on your page. Then link to the payment page, directly. Also called cookiestuffing. But in this case used for good.
There are some more complicated variations that do switch off any sounds, etc, the vendor may have using javascript. But you'll probably have to spend money on a programmer to do it. I did that anyway. I am not aware of any software that could possibly do this.
Do test the process and make sure your affiliate ID shows up at the bottom of the payment page the minute you created your page. You do this by going on your page, then clicking on the buy now button and checking the bottom. If it shows your affiliate ID, it's good to go.
Also, I am not entirely sure if this is still possible. As this was the way I did this a couple of years ago. But I cannot imagine them having something against it if you are using it to promote one product with your own LP just because it works better. They probably still want their affiliates to earn well despite their changes.