Note: The product design is such that the entire PCB / battery assembly is a replaceable part, not just the batteries, so this is a hack, not a manufacturer designed battery change.
You will need to have two new 2100mAh (or better) NiMH (Nickel metal hydride) batteries, a soldering iron, small flat head or trox screw driver and cutters.
1. Start by removing the little cover around the charging socket using a thin blade screw driver.
2. Un-clip the side grips, pulling outward from the bottom end. (The grip, hook over at the razor head side).
3. Remove the 4 housing fixing screws, using either a small flat head or trox screw driver.
4. Separate the 2 body halves, pulling them apart from the bottom edges. (They hook over at the razor head side). Work close to a tabletop, being careful that the internals do not fall out.
Step 1: Remove Circuit Board
Take note of the terminal directions of the batteries, as you should replace them in the same direction.
Note: The batteries in this razor have already been changed and therefore they are showing the new batteries already soldered in place.
I used a Dremel rotary cutting tool, but a file or hacksaw blade can be used.
Remove batteries and discard them responsibly.
Replace with 2 new NiMH rechargeable batteries, by soldering them back in the same terminal direction as the originals.
The close up images show my dodgy soldering of the tabs back the batteries. The terminals on the head side are easy to work with, but the terminals on the socket side are trickier (as there is very little space to work in).
Step 3: Re-assemble Housing.
Be aware that if you have too much solder on the batteries, then the motor terminals will make contact with the batteries and will run without the switch being in the ON position.
Good luck and keep those good, easy to fix appliances out of landfill!