Step 1: Supplies
As far as I can tell, all NiCD cells are 1.2 volts, and this one appeared to be almost exactly the right size. Since the toothbrush can hold enough charge when new to go for a week without recharging, we figured that even if these didn't exactly match the capacity of the original NICD cells, they ought to work.
Because the device was designed for NICDs, you ought to replace the battery with a NICD.
Beyond that, you need a soldering iron, solder, maybe an X-acto knife, some long-nosed pliers, a hemostat (we used a paperclip instead), and some electricians' stable.
Step 2: Take the End Cap Off the Toothbrush
The "wrench" for unlocking the base of the toothbrush is on the back of the charger.
Get a good grip on the toothbrush, push it onto this "wrench", and give it a slight twist while pushing it solidly into the charger. It takes little effort and about an eighth-turn to unlock the toothbrush bottom. When you feel it pop, gently remove the toothbrush. If the base of the toothbrush sticks to the charger, get a screwdriver or other small instrument in there and gently pry it loose. Don't try to pull it off via the four thin copper wires.
Step 3: Remove the Innards
To be clear -- the entire thing comes out, so push the steel rod where the brush attaches, as you disengage the bottom end of "the works" from the exterior casing. This does not require a lot of force. Once it's free, its just the friction of an O-ring seal at the top that is holding the works in.
Step 4: Remove the Old Batteries
Step 5: Solder the New Batteries Together,
First, and dumbest, solder the batteries together POSITIVE to NEGATIVE. The positive terminal has the bump on it, just like a regular AA. I laid the batteries out side-by-side, clipped the leads together, and soldered. Then just fold the mess together as tightly as possible and put a bit of tape on it to hold it together.
Step 6: Solder the New Batteries Into the Casing
It's a major boo-boo to get that wrong, so check it a couple of times.
As to how you get the battery tabs soldered to the stubs, all I can say is, I did the one in the middle of the casing first, folded up the tab, and then did the one at the bottom. The tabs need to lie nearly parallel to get a good solder join -- but then you can just bend the excess out of the way.
For what it's worth, the standard advice is, don't overheat the battery when you do this. How you'd know the battery is overheated, don't ask me. Anyway, the goal is to get solid solder joints between the battery tabs and the stubs of the tabs that are attached to the circuit board. No style points -- any way you can manage that is OK.
Step 7: Re-assemble
Now, here's where you may break one of the four small wires. (I did, and just soldered it back into place).
The hardest part of the entire deal is re-assembling the bottom. Hold the toothbrush upside down by the case, assemble the parts (with the "turning" part of the toothbrush bottom in the open (one-eight-turn-askew) position. What you have at this point looks like an exploded diagram of the bottom of the toothbrush. Make sure the four thin wires look like they are resting comfortably. Now hold the charger wrench facing downward, engage the upside-down toothbrush with the wrench, gently compress the mess, and turn it back one-eighth turn to tighten.
If all goes well, hey, that's it. If not, it'll take you three or four tries (as we did). We (my dad) broke one of the wires at that point, had to solder it back -- might be worthwhile taking a look at those before you start this step, just in case.
But all's well that ends well. Plug in the charger, put the brush on the charger, and see if it'll charge. Blinking light? All is well. After a couple of minutes, you can briefly turn it on to verify that it works. Then let it charge.
Step 8: Epilogue
Bottom line: $5 worth of batteries, $3 shipping, and an hour of labor saves a $90 toothbrush. No idea how long this will last, but it seemed worth the gamble.
Finally comments: Probably should have replace the O-ring seal at the top while I was at it.
And, if you're going to be photographing your toothbrush for viewing on the internet...
...Clean it first.