If you are using WebSockets for communication between Node.js and WebView then you can setup the server so that it accepts only one connection at a time. Also, when app starts you could generate random hash and pass it to Node.js and WebView environments. When Node.js server receives request that does not contain the valid hash then just drop the connection.
AppJS does not use http connections. It only simulates it. It uses a custom scheme (appjs://).Whenever a request with this scheme is made, AppJS routes it to your javascript code in node.js.