After cutting off the damaged part of the cable, insert it into the plastic stopper cleaned in step 8. This way the insertion is easier than making it at step 12.
If you dare to desolder the wires from the board to solder the new ones directly instead of attaching them to the cut segments, be EXTREMELY CAREFUL not to short the Yellow Capacitor next to them. I shorted it with the soldering iron by accident and a spark flew. When I assembled back the charger, it was dead. Had to buy a new one. Soldering the wires directly to the board is better, but definitely not worth the risk. :(
You could cut the cables and solder the new batt's to these, but I'd make sure the total length of the splice is the same to the original. Also use the smallest-diameter heat-shrink tube to insulate so as not to make a bump that prevents the trinket to close properly.
Excellent guide. If you trust your skills, you can desolder the wires from the board but be very careful: there's a cap nearby that might be charged and give you a nice zap.
There is a metallic ring inside the plastic. That little devil has two small claws inserted into the plastic. What I did was dig with the tip of my soldering iron at low temp (just enough to soften the plastic) and pull it off with pliers when I found them. After that it's pretty easy to clean up the hole to let the cable pass. When straightened, the ring and claws look like those donkey ears they used to embarrass bad students, in comics. :)