Actually it was quite easy, install the plugin "Remove slug from custom post type" to remove the '/product/' slug, no settings required. Install the plugin "SEO Ultimate" to remove the 'product-category' slug, in SEO Ultimate settings under 'Permalink Tweaker' check the 'Product Categories' and save. We use it for affiliates so cannot comment on other areas such as cart.
Sorry, this is not working...
/Kim