Interesting idea, I'm not sure if the iframe process will actually work. If they only have one product to sell you could always set up a separate copy of BV. I think BV licensing is free when a store has less than 11 products. So if you created a new store with just one product that might work. But if they're looking for something that's really co-branded, you would have to consider, what would happen if the shopper clicks other shopping cart links within the iframe. The user experience could become weird, i.e. if the shopper created a user account within the iframe they would have (perhaps surprisingly to them) a new user account created for your shopping cart domain.

Maybe a co-branding solution could work where shoppers would be directed to a co-branded domain for their shopping...maybe shop.company.com, where you deploy the single product version of BV.

But for a single product on their site, where shoppers will always just buy that single product, i.e. immediately check out the product once purchased, perhaps the easiest path of making a page on their site with a PayPal buy now button could work, unless there are other needs