Thanks for your reply again @luminus! I have a solution that works for me now. For people who come across this topic in the future, I used the following code to adjust the standard template:
remove_action( 'woocommerce_before_single_product_summary', 'woocommerce_show_product_images', 20);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_title', 5);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_rating', 10);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_price', 10);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_excerpt', 20);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_meta', 40);
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_sharing', 50);
remove_action( 'woocommerce_after_single_product_summary', 'woocommerce_upsell_display', 15);
remove_action( 'woocommerce_after_single_product_summary', 'woocommerce_output_related_products', 20);
Indeed, this does effect all product pages, but for my site this is the intention. I placed this code in a own plugin, but off course you can also place it in the theme functions.php file.
The warning “Shortcode “Single Product Page Add To Cart”. Please view Product after assigning Custom Template” was from the plugin ‘Woocommerce Single Product Page Builder’. I used this plugin to try to adjust the product template, but that didn’t work out for me.