Why build a second power supply just to run the relay? How about driving a 24V relay from the existing power supply output via a suitable zener? With a zener chosen to drop enough volts to give nominal relay voltage when PSU is at working voltage, the relay will operate a little earlier than that, but by then the initial surge will be over. Even simpler, use a series resistor to give nominal relay voltage at PSU nominal output. I'm not convinced that surge protection is needed at all (my system works fine without but I chose my input MCB carefully so nothing trips, and that's the only reason why you need to bother) but if it is, make it as simple as possible. I've never used the NTC approach, partly because it looks as if you have to choose carefully to match PSU current draw, which is pretty variable driving a CNC machine.