First, we'll need take measurements for how long the wires will need to be to reach the placement of the LEDs to where you plan to attach the coin cell clip.
In our case, we'll need the wires to reach from our eyes down to the back of the shirt. We made sure to add an extra bit of slack to compensate for curves around ears. We measured about 37 cm long to reach from the back of our shirt collar, around our ears and to the ends of our eyebrows.
We used wire wrap to connect the LEDs because its thin and still has just enough strength for repeated use. We also tried using the ultra thin magnet wire. It definitely blends into skin better, making it basically invisible, but it will break after repeated use. You could try to strengthen it by doubling up and combining two wires together.