Tax per site

[ryssbowh]

I have a multi site instance with two sites : Retail and Trade.

The products are the same between the two, some will be available in one site, some in the other and some in both. The pricing is also the same except that the tax category will be different for the trade site (no tax).

As far as I can see it's not possible to apply a tax category to a site, only to a product type.

Do I need to duplicate all products to achieve this ?
Or any hint at which point in the application I can hook through a custom plugin to change the tax category of the order items ?