Using this blog as reference guide – perhaps slightly easier than bookmarking topics, and in case the internet eats the posts.
Per this thread, to delete an order, do the following:
SET @orderId = '100000001'; SET FOREIGN_KEY_CHECKS = 1; DELETE FROM sales_flat_order WHERE increment_id = @orderId; DELETE FROM sales_flat_quote WHERE reserved_order_id = @orderId;
This works in Magento Community v 18.104.22.168 and Magento Enterprise 22.214.171.124. It deleted all mention of the order from the dashboard/reports.