Hooking a wifi thermostat to a 2 wire boiler
How old is the home? It is not impossible that the cloth wiring could be asbestos based, so work safely.

As long as the wires are NOT 120V wires, you should be fine. Some newer thermostats (like the Nest Version 3) do not require the C.

You can run a new wire, if you do so, and it is as easy as you imply, you could always replace the old wire.