Hi, Charles.
Lisa here from the Shopify Support Team.
Here's the first step of relinking/ hiding the add to cart button for this one product:
However, to relink the add to cart button to an external link does require an Expert coder! (As you may have seen in other forum posts)
The good news is, it is common for merchants to link to external links lately with all the available affiliate programs. Most have found a way around hiring a developer by doing the following 1. Remove the actual add to cart button 2. Create a 'new button' straight from the product page.
Here's an example of a 'new button' on Brooklyn theme:
What was done here was the "Add to Cart" text was temporarily updated in the language section of the theme. Then it was screenshot and cropped for an exact replica of the button with suitable text.
After retrieving this button image, next step is to follow these instructions to remove the actual add to cart button and create a new product template.
Once you have created the product template, within your product listing on the right-hand side you will be able to select the new product template:
From the product page, to add the 'new button' click the image icon in the bar, add the button image. Then follow these instructions below to link and centre: 
Hope this helps you easily achive linking externally from your one product page! This way is also great for updating the links when need be as it saves you going into the code every time and changing the template.
Let me know if you have any questions.
- Lisa