Some proxies block Websocket Connections by default for unknown URLs, even for port 443. Don’t ask me how I know :D

You can setup Apache Guacamole on your server. It uses Websockets by default, but it also has an automatic fallback to plain http/https. It will be ultra slow, but at least it will be working. It will behave like any other website, so no security risks for your company if they already have a proxy server to monitor your Internet traffic.