Please see the diagram that is showing a working wireless switch with single wire connection.
Yes, of course there are electronic switches that work in this "two wire" manner. In fact, your common dimmer does. If you want some "intelligence", then the device needs to have two modes for obtaining power, one for deriving a very small current - insufficient to light the lamp - at the mains voltage when the switch is "open" and efficiently transforming this to a significantly larger current at 5V or so for the "intelligence", and a second mode for deriving power from a rather small voltage drop but with significant current when the switch is "closed". In essence you require two (switchmode) power converters, a step-down from mains to 5V and a step-up from 1V to 5V.
In practice, these electronic switches generally are simply designed instead to use extremely small currents, especially in the "off" mode. Even so, they tend to be incompatible with modern LED luminares which use and respond to very small currents anyway, so that they will tend both to "cipher" and glow dimly when turned "off" and may even provide insufficient current when turned "on", to properly power the electronic switch and so cause erratic operation.
In any case, all such "electronic switches" must be considered to make the circuit "live" even when apparently switched off.
In general, an Arduino requires quite a bit more current to operate (fully) than such ASIC devices, and will be rather impractical.