How to use the shop to sell things via 3rd platform? Selling via 3rd party?

I currently use a 3rd party to sell my product/ services. This 3rd party connects to stripe but, this software service manages appointments, scheduling, recurring payments, etc.

What i have been doing in the past, is have a button on my site. that button opens a link to the 3rd party site for payment. they create an account and can manage their appointments, payment methods etc. 

How do i create a shop that does this?

Does this 3rd party provide a button builder of some kind like Shopify or PayPal? That would be one way to go.

If the 3rd party provides a customized URL of some kind that is another way to go.

Both of these options would require a certain amount of custom code to alter the look and/or behaviour of a product detail page.

Without more detail on what services your third party provides there isn't much we can provide in the way of a more specific direction to go.