Using a led bulb in a sanctuary lamp

I want to replace the oil in a sanctuary lamp with a small led bulb that runs off a battery but have no idea what size battery and how long it might last, and whether this is possible. I would like to hide the battery into a hollowed out candle. The sanctuary lamp is blue so the amount of light is not required to show anything other a tiny but visible glow. I do not wish to run transformers or wires up the wall as this would be ugly. Any suggestions please and thank you. Father Mark