Transfer power through wooden table
It's possible when the candelabra isn't made of metal – and that requirement would kill all the romance, wouldn't it? But then, battery powered candles already do, I think. Makes me think I was eating at Legoland Burger King.

You had to install an ironless magnetic coil below the table, and connect it to a power amplifier feed with a frequency of roughly 15kHz. Install another ironless coil into the candelabra bottom, connect its terminals to antiparallel LEDs. You are done.

Why 15kHz? Because the amount of copper needed for the receiving coil drops significantly with frequency, so you can have a smaller coil. And because 15kHz is something an audio amplifier can deliver. You could even make a CD with the required signal.

Why ironless? Because iron wouldn't help you anything at 15kHz.

And why can't your candelabra be made of metal? Because the 15kHz transformer would induce eddy currents in it, making it heat up like a pot on an inductive stove. Well, not so much, but it draws power which can't be used for the LEDs.

(A better setup would indeed feature a magnetic core, but made of ferrite and at least 2" in diameter. Very costly and you need the same in the receiver.)