As Thomas M. DuBuisson stated you just need to compile the entire project into the final binary and copy that and all the project files (html, js, etc.) over to the server. Because the entire project is compiled and includes a webserver those are the only files you need.
So to reiterate the steps.
Get a different machine with the same operating system that can compile the framework. In my case I had a local virtual machine do it.
Compile the entire Snap project using that machine.
Copy the compiled project (binary, and web files) to the other machine (that can't compile).
Run the binary. It includes a server so there should not be any other dependencies. Unless your project utilizes dynamic libraries. In that case copy those over as well.
This works because the actual Snap Server is included with the Snap Framework application when you compile it. The answer is actually much simpler then I thought, and I was just overcomplicating it.