I don't believe the internet has previously figured this out. Google searches I've done have suggested that this is impossible without visible splicing, and suggested buying an aftermarket replacement. This is a problem given the plethora of N64 controller colors, and if you're OCD enough that aftermarket connector staring at you, mocking you, might make you hang yourself.
But I've finally popped open a connector without damaging it. Ok, I slightly damaged it, grabbing it with a vice, drilling out the visible tab, blowing WD-40 into it, whatever Here's what worked. I obtained some thin/flat metal from the seal on a bag of cookies I was throwing out. I gave the ends of the metal a slight bend so they point outward, and pressed them into the tab slots as hard as possible (don't hurt yourself, use some pliers). Then I folded down the excess metal just to get it out of the way, and I carefully wrapped the black tip with a whole bunch of packing tape. The tape is for grabbing, so go nuts. Once taped up I grabbed the tape in one hand and the connector in the other and pulled it apart, it required twisting, rocking and a lot of force to pop it apart. But far less force than I applied to it with other brute force methods I tried.
Now I just need to go to the Home Depot and pickup some 3-wire cable. IIRC they had some red stuff I thought looked pretty for like 10¢ a foot