You could add an additional shipping cost by testing how many of the specific products_id is in the cart ...

In the function quote area of the shipping module, you could test for how many of the specific products_id are in the cart to add an additional charge ...

Example, if the products_id is 27 and you want an additional $5.00 per quantity:
global $cart;
$extra_shipping = $_SESSION['cart']->in_cart_check('products_id', 27) * 5.00;

Now add that to cost ...