Woocommerce – Change the template?

The dropdown box that you are talking about is for custom WordPress template that WordPress supports by default.

In order to override woocomerce template e.g. single-product.php
what you have to do is to create a folder with name woocommerce inside your theme folder e.g.

/wp-content/themes/{your_theme_name}/woocommerce/

and copy the file from /wp-content/plugins/woocommerce/templates/single-product.php into your theme’s woocommerce directory e.g.

/wp-content/themes/{your_theme_name}/woocommerce/single-product.php

Now its properly override and you can make changes in single-product.php within your theme.

This way your changes will remain intact even if you update woocommerce plugin.

To know in detail about woocomerce template overriding see this link

Edit:

Declaring WooCommerce support in themes

Declaring WooCommerce support is straightforward and involves adding one function in your theme’s functions.php file.

function mytheme_add_woocommerce_support() {
    add_theme_support( 'woocommerce' );
}
add_action( 'after_setup_theme', 'mytheme_add_woocommerce_support' );