Sunny here from the Shopify Guru team and I'd be happy to offer a few suggestions for your specific situation.
We have an app on our App Store called Vendor Payout that allows you to easily split your sales between third party vendors, designers, artist, suppliers, etc. The app was originally created to save our merchants lots of time and effort running reports and splitting royalties between multiple vendors but I think it can work for your situation as well.
The app offers a 7-day free trial which is great to see if it fits your needs, and for $30/month you get unlimited vendors and logins, the ability to assign each vendor a percentage or fixed amount and it will auto-calculate all orders.
The downside is that it's more of a reporting tool and does not have the capability of paying your third party their percentage directly in the app. In the app's FAQ page here, they explain that many store owners use PayPal or Quickbooks to transfer funds instead. Although you cannot pay out directly through the app, a great benefit is that the third party vendors can login and see all orders sold with their product so everything is transparent.
On the bright side, it may actually be more convenient for your vendor to receive their funds in bulk, perhaps monthly or bi-weekly for example, instead of multiple times a day which can be hard to keep track of.
If you're looking for something more custom, it does look like this app takes customization requests for an additional fee. Alternatively, you can check out our Shopify Experts where you'll find skilled people and companies who can build this functionality for you.
I'd love to hear your thoughts on the app and please let me know if you have any question at all.
Sunny | Shopify Guru