The way the search works is if WooCommerce is not active it uses the standard WP get_search_form() function.
If WooCommerce is active then it makes use of the theme’s custom search function – trusted_woocommerce_search_form() – to search WooCommerce products.
The trusted_woocommerce_search_form() function can be overridden in a child theme. Look in extras.php line 817 to 841, copy the function to the child theme’s functions.php file and remove the part that displays the WooCommerce categories dropdown (line 823 to 833).
Now the important part to change is line 835: <input type="hidden" name="post_type" value="product">
where you should change ‘product’ to the name of your custom post type.