Powering the UNO (wrong device for a wearable - use a Nano. In fact, use a Nano in preference to UNO for everything for which you do not have a specialised UNO shield) from a 9 V battery is total nonsense. It runs on 5 V - 4.8 will do just fine - and the on-board regulator is pretty useless.Connect your battery pack via the switch to the terminals of the WS2812 strip using twin cable ("figure 8"). Now connect all three connections from there back to the Arduino 5 V terminal with a 3 wire ribbon. This fulfils the requirement that power wires run together as a pair and signal/ control wires run together.