I've submitted an edit clearing up where to start the pry tool. Please folks, if you encounter something like this don't hesitate to remove bad information! With the contradictory instructions here I ended up starting on the left and piercing the cable like so many before me, which is very frustrating.

Applying force on the top of the outer case as in the second image didn’t work very well for me. But the outer case has a hole where the charger terminals exit the bottom of the shaver. I was able to remove the inner housing by holding the outer case and pushing in on the recessed plastic surface around the terminals with a small screwdriver. On reassembly, the housing snaps right back in.