Sending the power over a single wire requires you to transmit it via an alternating current and have a credible counterpoise at the other end. If you go to a high enough frequency you could use half of your ball covered in mesh capacitively coupled to the atmosphere and then use HF recitifiers to extract power from the RF signal you radiate down the wire. It may be quite possible but would also radiate a lot of RF into the vicinity that may interfere with other parts of your project.
Unless there was some other compelling reason I would use a co-ax cable thin enough to look like a single wire or perhaps a mixed core multistrand wire such as used in typical eadbud headphones. They have two, three or four isolated groups of wire strands (often coloured by group) to take the signals from a cell phone or MP3/4 player to the earphones and mic and possibly mic switch.
If you just need to do this once and for a single demo then the battery solution proposed could work, a IR receiver as used on cheap indoor RC helicopter may be flexible enough to work, radio is also simple if you select a small module.