I too like the two tube approach. So the outer tube rotates and the inner tube is stationary. Telescoping brass tubing is inexpensive and available by the foot at most hobby shops. Then the power source for the lights can be below the surface and tied in with the motor so lights come on when motor spins. Two wires run up the stationary tube to the LEDs which can be centered in the sphere for more uniform lighting.
I'd think having the power source below will give more options on LEDs since a single AA is only 1.5 Volts and presumably you're thinking white LEDs. Many more options on white LEDs if you have more than 1.5V available.
Then, rather than lowering the motor voltage, I'd gear the drive motor. This is probably the easiest way to implement the two-tube approach. So a larger gear goes around the outer rotating tube and the motor has a smaller pinion gear. Plastic gear pairs are inexpensive on eBay or from a broken toy. Gearing increases available torque as speed is lowered. So even in you end up electrically reducing motor voltage via diodes or whatever the gearing will make speed adjustments easier.
If you want to stick with the battery in the globe, did you consider a latching reed switch? You turn the switch ON with, say, the North pole of a magnet nearby and it stays on until you bring a South pole nearby. These are somewhat fragile devices. You can also design a transistor-level circuit that behaves as a latch though I'm speculating the "problem" is one of turning on the light with some kind of momentary trigger (switch, motion sensor, light, whatever) and then turning off the light with another momentary trigger. Of course any latching circuit itself consumes power which affects battery life.
