Can I use my own shipping provider for my Trade Assurance order?

Yes. The shipment of your Trade Assurance order depends on the agreement between you and your supplier. Please negotiate with the supplier if you want to use your own shipping provider. 

A warm reminding:
If the Trade Assurance order is placed to choose to export via Onetouch, you need ask your provider to export in the name of Onetouch. You could ask for your supplier's help about it.