How do I remove the edit buttons from the order confirmation page?

[lat9]

... or, if you still want customers to have multiple addresses that they ship to, just not changeable from checkout_confirmation ...

You can edit/create the file /includes/templates/YOUR_TEMPLATE/css/checkout_confirmation.css and add the following lines:

#checkoutBillto .buttonRow, #checkoutShipto .buttonRow {
  display: none;
}

That will simply "hide" the buttons from the display.