The black Apple pro mouse have some well known issues:
-Only one button
-Too flexible and short cord, which have a very high failure rate.
But I love it's sleek minimal design.
Mine has broken too, next to the mouse end and also at the USB plug. Since to open and to nicely refit the USB plug seems impossible, I decided to change the USB cable completely.
Step 1: Taking Apart
There are a couple well detailed guide on the web about how to open and refit an apple pro mouse. But all of them only helps you when your USB cord broken next to the mouse's end. My cord has been broken on the other end too, so I have to change the whole cable. Also, I was fed up a bit with that very short cord.
Step 2: Color Match? Nooo...
I sacreficed a cheap USB mouse for get it's longer USB cable.My biggest problem were that no USB pinouts data about inside the mouse nor on the web (or well hidden).
The standard USB built up from four wires:
BLUE(or BLACK), GREEN, RED, WHITE
In the apple mouse' original cord are five wires ( see picture, from left to right):
SHIELD, BLACK, GREEN, BROWN, WHITE
Heureka! I ignored the shield wire, I paired the colors to it's nearest on the spectrum (Blue-Black, Green-green, Red-Brown, White-White), and resoldered them.
But as I tought at the begining, Apple always change the rules a bit, NOT WORKING, no success...
Step 3: A to A, a to B, Etc...
OK, I had to play a patience-game, if I want to give a new life to this mouse. Because the original cable were broken too, I cannot check the pinouts through the USB plug.
I started to connect a cables to a different cables, and check them at every settings on my Mac.
There were a little help when I saw the LED is lighting, I knew at least the +/- 5V cable is on place.
Step 4: The Pinout
RED to WHITE
WHITE to RED
GREEN to GREEN
BLACK to BLUE
I ignored the SHIELD cable.
I can not guarantee that this pinout will work with your new USB cable too, but there is a chance ( I checked the sacrificed mouse internal pinout and on one another -both from the same manufacturer- and there were different pinouts too!).
Step 5: Black to Black With Extras
Check those giudes about how to put/glue the mouse together.
On the end I have a black mouse with a new, long, less flexible black cord.
Thereafter I made a genuine apple keyring from the faulty USB plug too. Just for fun.