There are three possible solutions I can think of, assuming you want a switch that works with all kinds of connected electrical devices and not only light bulbs.
Use (at least) a third wire for power supply, if possible.
Use a battery. This has the drawback that the switch might not work if the battery is empty.
Do something fancy and recharge the battery while the switch is on. A slight voltage drop is usually ok also for other devices than light bulbs (see below), but it ensures that not current flows if the switch is turned off. If you want to be on the safe side, use induction*, but that is not something I would suggest for a consumer product without hesitation.
* There is a corresponding paper called "Energy Harvesting from Electromagnetic Energy Radiating from AC Power Lines" by Vikram Gupta, Arvind Kandhalu and Ragunathan (Raj) Rajkumar (https://users.ece.cmu.edu/~vikramg/docs/hotemnets11.pdf).
If you are restricted to classical light bulbs or something similar, you can exploit the fact that if a few mA flow through a light bulb it will not light up. The filament works as a simple conductor. So you have to design a power supply circuitry that has a high voltage drop, but consumes only a few mA.
Then when the switch is turned on you have to switch to a power supply circuitry that has a low voltage drop so there is enough left for the light bulb. For classical light bulbs this will result in a non-perceivable drop in brightness.
Instead of a steady current you can also exploit the fact that very short pulses (either on or off) will also not be perceived, but can be sufficient to power your circuit.
As written above, this is only possible because of the way a light bulb works. If you connect for example a device with a switched power supply you might get really strange effects.