I do believe you selected the webserver configuration "Nginx & Apache" from the webserver solutions offered by CWP.
In this case NGINX can't be removed/disabled for some specific users completely because the option "Nginx & Apache" configures NGINX as reverse proxy. It means NGINX listens the ports 80 (http), 443 (https) and gets all HTTP/HTTPS requests. In case the request can't be handled by Nginx it goes to Apache.
In your case you can create some "dummy" nginx template for Nginx. It should just accept the HTTP/HTTPS requests and pass the requyests to Apache without any doubts. Then use "WebServers Domain Conf" to enable the created template for the specific domain/user.
Let us know if you need further assistance.