I think I can help. The Carro app allows you to ship products to influencers and keep track of each transaction within Orders, as a free checkout so that it doesn't affect your accounting. It can also help you discover influencers to work with, making your influencer campaigns streamlined and simple. It's also free, so it's a great app to get your influencer marketing started.
The alternative would be to create an order in Shopify, then add a discount of 100% to the order so that you can process it with Shopify shipping.