I unfortunately didn't take many in-process pictures--I didn't think of making an instructable out of it until later--but fortunately this is a very understandable process. I started by carefully taking all of the screws out of the plasma ball base, then prying the base open. All of the electronics are attached to the bottom portion, and only a single insulated wire extends up the shaft into the center of the ball. I pulled out the wire, removed the base and set it aside.
The glass sphere of the plasma ball is sealed, essentially like a giant light bulb. The biggest challenge of this project was cutting away most of the plastic base with a dremel tool and wire cutters without nicking the fragile glass of the plasma ball. I covered the bottom of the ball in masking tape to improve my odds of success. After about an hour of patient cutting, I was left with a 1 cm collar of plastic around the base of the sphere.
Next, I removed the hanger from the brass lamp, as well as the lamp glass, the socket and a large washer that was holding the threaded lamp pipe in place. I used clear silicon to attach the globe to the top of the brass lamp, then concealed the electronic base in the lamp base as well, being sure to allow clearance so it wouldn't short out. The picture below was taken before I concealed the electronics in the base, while I was testing for shorts.
Finally, since the on/off switch was sealed inside the base, I plugged the lamp into a wireless christmas light switch so I can turn it on and off with a remote.