Since you say "simple", use phpmyadmin to make a copy of the database when your cutoff time comes, and then just delete the orders in your live database.
(you may need to use some other tool to create an empty database first depending on your host, create priv is often absent in phpmyadmin on shared hosting)
If your shop evolves a lot, that is also a good time to make and save a backup of your code too.
Kobra makes a good point to consider. If your shop is not allowing / requiring customers to make an account in the first place, then this is no issue.