Apart from obvious problems like ground loops or insufficient power to run the device, switching DC PSUs does not affect the sound in any way. Also, this DAC measured transparent with the original PSU, so if there were any audible difference, it could only be worse.
It's helpful to know about the problems of sighted testing, human bias and how small level differences affect the sound impression you get from a device. You should look into those topics.
no man ifi has noise floor is like 20-30dB lower than the stock and spikes are at 1uV instead of the stock which are probably horrible the difference in power deliver are so huge it impacts the clarity a lot - its the same power rating for both but.... on the ifi i was able to drive it on headphones so much it became a hot plate after couple of hours (was at most warm with stock)