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.
what you have to do is to create a folder with name
woocommerce inside your theme folder e.g.
and copy the file from
/wp-content/plugins/woocommerce/templates/single-product.php into your theme’s woocommerce directory e.g.
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