What I would suggest you do is to create a draft order and apply a 100% discount to it. This will remove the product from your inventory while at the same time will not add incorrect figures to your reports. You'll also have the option to purchase a shipping label so you can send the item to the influencer.
The app Carro can make your free influencer orders super easy with Influencer Checkout. The Carro app allows influencers to request the products that they really want, then you can approve or deny the product requests in your Carro Dashboard. If the request is approved, it is automatically created as a free checkout order in your Shopify orders and marked as coming from Carro. Then it can be fulfilled through your normal processes.
And Carro is a free to use app! I hope Carro can help with your influencer marketing campaigns. Let me know if you have any questions.
I created these draft orders but also marked them as paid/fulfilled and now they're tracking towards our average sales amount, which we don't want.
If I save them as drafts and unpaid will it not count towards the average sales amount?