I do not think a toroidal inductor would be ideal for this type of situation. The magnetic flux lines are most densely packed in the center of the hole running parallel with the axis of symmetry:
If it were resting on top of the xLED, the brunt of the field would be running perpendicular to the coil in the xLED and no power would be able to transfer. A toroid would make a cool necklace, though.