No, I'm sorry, that Anderson is not the typical humbucker. I was only showing it to demonstrate how much easier that particular one was to work on than a typical humbucker. If they were only all designed that way, things would be much easier!!
The inside of a McCarty pickup will look sort of like this when you take the bottom plate off:
This is the inside of a HFS but the McCarty is constructed the same way, especially if yours is a 4 conductor version. You'll have to remove the magnet, spacers and the tape around the coils. Each coil will separate from the other, so it can get out of hand quickly.
I haven't gone this far so I don't have pictures, but at this point you'll have each coil and each one should have two wires coming off it, which should be attached to the main lead wire, and from there you can figure out how to replace the lead wire. But I'm telling you,
if you have your doubts about doing this, please don't ruin your good humbucker.
The best resource on the Internet for modifying pickups is the Seymour Duncan official forum. I would suggest doing a lot of reading over there and figuring out how to do these things and then once again, practicing on some cheapies like SE pickups or some old Epiphones or going down to your local repair shop and asking what sort of no-name budget humbuckers they have left over from repair jobs that you could buy to work on.