To have freedom, you need a central server that both connect to. The server can relay the data to the other one. I don't have enough knowledge how to do that in the server.
Websockets do not have to be slower than TCP. The delay will not be in code, but in the online timing. Speedtest.net tells me that my ping is 12ms (that is not very fast). With two devices and a central server it is at least 24ms.