Wifi light switch needs neutral wire. Why? AND Can that wire be a skinny one?
Because unlike a normal switch, the wifi switch needs power, so it needs a neutral wire to complete a circuit at the switch between the unswitched hot wire and neutral for that power.

The neutral wire to the switch cannot be a light-gauge wire (at least if you are in an area subject to NEC codes; likely similar elsewhere in the world) because codes are based on what the circuit breaker protecting the circuit can supply when choosing wire size, so for 15A circuits the wire must be 14 Ga or larger, and for 20A circuits the wire must be 12Ga or larger. Smaller wires could overheat to the point of causing fires (without tripping the breaker) in the event of a fault condition, even if the normal current in them might be a matter of a few milliamperes. 

I regard wifi switches (and thermostats) with the baleful gaze that only a network admin can view such things askance with, but I gather that there are units arranged in such a manner that the actual switch/relay can go in the ceiling where the light fixture that the switch loop originates from is, and the switch loop wires can (without adding any) be repurposed to operate the remote switch in the wall, no longer actually running the power for the lights through there. This type of unit will probably be much easier to install than to attempt to add a neutral wire to a switch box without one.