The good news is that the hard part is over, and if you weren't a soldering pro before, you are now. Get your Adafruit switched CR2032 battery clip, Solder the four header pins in place. Clip off the two middle ones, they'll only get in the way.
Thread the free ends of the two wire twists through the large holes for a bit of strain relief and arrangement. Strip off a small amount of enamel on the remaining 4 ends, solder the negative wires to GND and the positive wires to SW.
With the wires outside of the holes, any movement in the wire is concentrated on the solder points, which is structurally weak. When threaded through the holes first, the movement is concentrated at the holes where the wire is much stronger, and any pulling on the wires will direct the force in direct opposition to the strength of the other wire, adding further strain relief.