What is the simplest possible circuit for a wireless on-off switch
Simplest way I know is using light, put a phototransistor into the circuit as a low-side switch and shine a light at it, it will turn your LED on. This is good within line of sight. You can make this a fun laser tagging game my shielding the phototransistor so only a head on laser beam would hit it.

If you have to use radio waves within a short range, you can look into TA7642-based AM receiver and a single transistor AM transmitter. Feed the output of TA7642 into a Schmitt trigger and control a MOSFET with the output of it. This is good within up to a few tens of meters, about covering your house and maybe include your neighbor in the range. If you have some elderly living within that range this can be a very Good Samaritan project.

For even wider coverage range, you may be better off using Wi-Fi or 3G and control your trinket using Internet.