Solder your on/off switch in line with your battery extension cable. This cable will provide power to both the feather and the LEDs, so solder in a couple more wires to split the power.
This is also a good time to shorten the extension cable to an appropriate length that will plug into your Feather and your battery when they're in place.
Add some heat shrink filled with glue to the female end of the extension cable, since this will get pulled when you remove your battery for charging.
Get out your 3 tactile push buttons. Gently fold down two of the legs on one side -- we won't be using these and you don't want them poking you through your gauntlet.
Securely solder a black wire to one leg of each button and a colored wire to the other leg. Gently bend these down to add stability and minimize pokiness.
Twist the 3 black wires together and splice in a 4th black wire. This will run to the Feather's remaining G pin.
Connect each colored wire to your feather's A3, A4 and A5 pins (also known as digital pins 17, 18 and 19).