It already feels unreliable and a 555 makes it even less reliable.
To use a 555, you need a voltage that is fixed (not from a battery) and good components. The 555 can do a frequency between 200kHz and 300kHz, that is no problem.
The frequency of the receiver coil will change with metal nearby, or a hand nearby.
If you can find out of it is legal, then you can order an existing version to try it out.
In my opinion, it seems a gimmick for something static to look at. You have to test if it is reliable enough for your project.
Can you modify existing wireless leds ? They have already found the optimum for frequency/costs/reliability.