Right now, in woocommerce the shortcode [woocommerce_my_account]
displays the entire "My Account" page with all the tabbed options.
I only want to show the order details (found under the Orders tab) on a separate page.
So, can I just use the woocommerce template orders.php
(woocommerce/templates/myaccount/orders.php) and use it on a blank new page or is there a better way to go about it?
Woocommerce has function woocommerce_account_orders() which includes Orders template. You can follow the below steps to display only orders on a separate page.
Step-1: Place below code in your theme's functions.php (Place in child theme if you have created).
Step-2: Place shortcode [woocommerce_orders] in any pages in admin side and check on front end.
Above Code will display orders if customer is loggedin otherwise it will display woocommerce's login/registration page.
If you want to hide "Orders" tabbed option which is on "My Account" Page then go to Admin Side and then Woocommerce > Settings > Accounts (tab) where you can see "My account endpoints", empty "orders" field there. It will hide "Orders" from frontend "My Account" page.
Edit: Make sure that you check on frontend loggedin as "Customer" user and that customer user has atleast one order placed otherwise blank page will display there.