Powering 5V Accesories
If your supply is regulated (put a 47ohm resistor across it and measure the AC voltage with a DMM; it should be almost nothing if properly regulated) then you can use it for both the Uno and the NeoPixels. The ATmega328P has a maximum input voltage of 5.5V, and the WS2812B has a maximum voltage of 5.3V, putting the supply within the proper range to run them.