Can I re-send order confirmation emails with Mechanic?

As of this writing, Shopify doesn't have a simple API for re-sending order confirmation emails. (If this is important to you, send an email to [email protected] and let the folks there know that this is affecting your business.)
However, you can use Mechanic to trigger order-related emails on demand (sample task), and you can re-use your email notifications from Shopify (documentation).