First of all, I apologize that there are not more detailed photos for this section. I decided to put this guide together after I had completed it. I'll do my best to explain, but please let me know if I can clarify.

Cut off old power adapter and keep the cable (with the shaver connector). This is black in the photo.

Cut off non-USB-A end of a USB-A cable and keep the USB-A end. This cable is white in the photo.

On the cut end of USB cable, strip wires. Ensure they don't touch during next step.

Plug power adapter to wall, then connect USB cable. Measure DC voltage between each wire and ground of connector (bare metal portion at adapter end). Note the 5V output and 0V output wires. There should be only one of each. (The other two wires are for communications. https://www.electroschematics.com/usb-ho...)

Unplug the power adapter. Cut off the exposed portions of the other wires. Those need to be soldered to the old power cable. Unplug the adapter. Note the 5V output and 0V output and cut off the exposed portions of the other wires. The 5V and 0V wires need to be soldered to the old power cable.

Strip the ends of the old power cable. Connect to the USB wires (area outlined in red in photo). Connect power adapter to wall and measure final output. The center tap of the old power connector should be 5V relative to 0V of the barrel of the connector. If it is -5V, you will need to reverse the connection.

Insulate each connection using shrink wrap tubing before soldering. Solder. Position and heat shrink wrap. (If not shrink wrapping, wrap both wires with electrical tape.)