HTTP and HTTPS listen on different ports (443 for SSL, and 80 for HTTP), so you will never have both listening to the same port. Currently, there is no way to tell cshttpd to stop listening to the regular HTTP port. However, an administrator can change the service.http.port to an undisclosed number.
Do not set service.http.enable ="no" in an attempt to prevent cshttpd from listening to HTTP. Doing so would cause HTTPS to fail also. Both service.http.enable and service.http.ssl.port.enable must be set to "yes" for SSL to be configured properly.