I think you should replace:
<a class="button ajax_add_to_cart_button btn btn-default alt" href="{$link->getPageLink('cart',false, NULL, "add=1&id_product={$product.id_product|intval}&token={$static_token}", false)|escape:'html':'UTF-8'}" rel="nofollow" title="{l s='Add to cart'}" data-id-product="{$product.id_product|intval}"
with:
<a class="button ajax_add_to_cart_button btn btn-default alt" href="{$product.link|escape:'html':'UTF-8'}" title="{$product.name|escape:'html':'UTF-8'}" itemprop="url">
This only changes the functionality of the button, it's up to you to change the code/css to aquire the desired look .