Send commands from cPanel website to client ESP8266
I don't believe you will have the capability to implement a Websocket interface on the GoDaddy cPanel web site.  I think you are limited to just serving up HTML content and associated files.  Websocket requires a server-side resource to talk to which you cannot implement.
I see nothing wrong with having a simple HTML page, that doesn't even need to really contain HTML that your ESP8266 can &quot;GET&quot; and examine and determine to turn your relay on or off.