Depending on your intended application a string of fairy lights might work. The diameter of each LED is less than 1/8″ inch. The units I linked to run on two AA batteries so rechargeable cells are certainly an option; though you would likely need to remove the batteries for recharging. They are also available in different lengths and power configurations.
You could also buy your LEDs individually in 1.8mm, 3mm, and 5mm sizes. All of which would easily pass through a 1/4″ inch hole. Wiring and powering them would be up to you though.
