Woocommerce: Calling different custom archive product template for searches

I am using the following snippet in my functions.php file to call a custom template for my Woo shop page. It is working fine.

add_filter( 'template_include', 'custom_shop_page_template_include', 50, 1 );
function custom_shop_page_template_include( $template ) {
    if( is_shop() ) {
        $template = get_stylesheet_directory() . '/woocommerce/archive-product-custom-shop-page.php';
    } 
    return $template;
}

However, this template also gets called for a search with "no products displayed".

How can I modify the above snippet so that the results from a search are displayed in a different template:

If shop = product-archive-custom-shop-page.php
If search = product-archive-custom-search-page.php