Hi!
In this case I would recommend to redirect to the WooCommerce results page, which should display the results from the WooCommerce engine, but perhaps with the correct layout and the Add To Cart button as well.
To do that, change the Show more results.. url option on the Layout Options -> Results Layout panel to: ?s={phrase}&post_type=product
Like so: http://i.imgur.com/Ls9Plxs.png
