Yes! You can create a free shipping discount for your clients.
Simply create a "credit" discount as described here: Creating Discounts.
*Please note that if you allow your clients to choose their shipping speed and rate at checkout, this discount will work on any of the shipping speeds listed. For example, the client would have the ability to choose overnight shipping at checkout at no cost.
You always have the opportunity to override the client's choice in shipping during the Lab Approval Process, however, keep in mind that the client has already paid for his or her chosen shipping rate.