We do recommend updating the firmware on the Wi-Fi module, http://docs.ghielectronics.com/hardware/components/spwf04sa.html has some steps on how to do that.
So to work with the source for the Wi-Fi driver, you only need the drivers repo. You can just add the SPWF04Sx project to your own solution, then add a reference to that project in your project (you may need to uninstall then reinstall the NuGet packages). Alternatively, just take the source files for the Wi-Fi and add them to your project.