Disney Infinity as a game isn't really my thing. However, tiny Yoda with a light-up saber definitely is my sort of thing! So, I picked up a Disney Infinity Light FX Yoda hoping to mod the figure to be battery powered. The default power source is an induction coil in the base and a capacitor in the figure. The process to convert the figure to battery power is actually fairly straight forward. Here's what you'll need to make this mod on your own.

[Parts]

1x Disney Infinity Light FX Yoda (or other character)
1x CR2032 Battery
1x CR2032 Battery Holder with Switch (I got mine on Amazon)
Heat Shrink Tubing
2x Pennies or other battery size spacers

[Tools]

Dremel or other rotary tool
Flat Cutting Disc
Cylinder-Shaped Cutter (194 High Speed Cutter)
Rounded-Cone Cutter (117 High Speed Cutter)
Soldering Iron
1200 Grit Sandpaper
Hot Glue
Needle-Nose Pliers
Diagonal Cutters
Wire Strippers
Vacuum or Compressed Air
Dust Mask
Safety Glasses

Step 1: Step 1: Opening the Bottom and Cleaning Up

The first thing you'll want to do is open the bottom of the figure. The pictures run you through the steps.

This is the bit I used to open the initial hole and then clean up and enlarge to remove the circuit board. I like it because you can either hold it at an angle to get a nice triangular cut or hold it perpendicular to carve a semi-circle channel.
As you look at the bottom of the figure, you'll see three tabs on the clear base plate. You'll want to make your initial cut just inside of those tabs. There is a channel molded into the base that I followed for the initial cut.
I made 2-3 passes around the perimeter cutting deeper each time until I had broken through most of the way around the circle. At that point I used the needle-nose pliers to break the center out.
The next step is to clean up the cut and extend the diameter of the hole beyond the edge of the clear tabs.
You'll know you've made your hole large enough when the circuit board can freely fall out of the bottom.

Notes:

This process and the next step generate a ton of plastic dust. I used an air compressor to clean all the dust off when I was done.
Cutting this kind of plastic with a Dremel can end up with melted plastic instead of plastic chips. If you can, turn the speed of your Dremel down. I used speed setting 2.
There is a rim around the edge of the clear plastic base. Keep this intact as it gives you more depth for the battery pack.

Step 2: Step 2: Remove the Circuit Board and Internal Posts

Next step is to remove the circuit board, grind out the internal posts to make room for the battery and slot the cap of the battery pack.

The circuit board leaves plenty of play in the wires so flip it over and snip off the wires close to the board.
You will note there are two rectangular posts, two very small posts and an x-shaped tab. These all need to be ground down. In the few of these that I've done I haven't had any issues with Yoda coming loose, so I wouldn't worry about gluing these.
Grind the posts all down to the level of the surrounding plastic or close to it. Be very careful around the wires.
By default, Yoda's saber is clear. I like a matte finish instead as it makes the whole blade glow better. To achieve this, carefully sand down the saber with 1200 grit sandpaper.
Finished saber. You apply a very small amount of oil to make the finish less cloudy.
The battery case is hard to open when it's installed in the base so I slotted the cover with a cutting disc. This will let you use a screwdriver to help replace the battery.

Step 3:

Now it's time to install the battery pack and finish up the build.

Test fit the battery pack. It should sit flush in the base and not extend above the outer rim. If it does, you may need to remove more plastic inside the base or plan to add small feet.
The battery pack is fully recessed.
The battery packs I purchased were intended for two CR2032 batteries. This was more voltage than the LED needed, so I used two pennies as spacers. You could also use any battery-sized metal spacer (eg washers, etc).
Touch the leads to the wires on the figure and determine which lead should be connected to the black wire on the figure. Mark it with a sharpie.
Solder the wires and cover them with heat shrink tubing. I wrapped one wire with electrical tape and then used the tubing around both wires.
Determine a good layout for the wires and battery pack. Make sure you'll be able to replace the batteries and also reach the switch. Once you've found a good placement, glue the battery pack in place with hot glue.

Step 4: Step 4: Wrap Up and Comments

Jedi Master Yoda is now ready to protect your desk against the Dark Side!

[Final Notes]

I tried USB power as well. This works, but I worry it may shorten the life of the LED.
I have no idea if this ruins the figures for use in the game.
I assume this same process will work for the other figures but I haven't tried on any of them.