Need a "nano-powered" or wirelessly powered LED system - very small physical size

I am in need of a product that would preferably provide power wirelessly (via RF, wifi, etc) to individual LEDs that are housed within a small plastic space. I've included an attached sketch to give a general idea to the overall concept. My preferred product would be as follows: wireless transmitter is located underneath a plastic "base plate" that is very thin (approx. 1/16") and approx. 12" x 12" square. This size could change, however it should be used as a reference. I would prefer that the wireless transmitter not increase the thickness of this baseplate significantly. The LEDs will be housed within a very small plastic space, approx. 5mm x 5mm x 7mm. The thickness of the outside wall of this housing would be approx. 1mm or less. The wireless LEDs will need to be able to light and power up within 3 to 6 ft. from the baseplate. The physical size of the LEDs can be very small (as they'd likely need to be due to my size restrictions) but they would need to be able to be visible in daylight environments within that 3-6 ft range. I do not want the light to be so weak that it only shows in the dark. Each LED receiver/housing will contain only 1 LED, but I would like the transmitter to be able to power multiple LED receivers at the same time. The LEDs may also be different colors, so the power supply needs to be able to power red, blue, pink, white, purple, orange, etc LEDs... A rechargeable LED option would not work, as we cannot require our users to pull the LED receivers from their assemblies and plug them on to a charger to power them. Also, a super capacitor option would likely not work because the LEDs need to be able to last a year or more... perhaps indefinitely if possible.