@SergeP, I think that for a clock the startup noise is not really a problem, because a clock is usually started rarely and tried to be kept up as long as possible. To avoid noise, you could think of adding some power control of the neopixels.
According to NeoPixel WS2812 data sheet (as attached as .pdf), control logic and LEDs have separate power supply. That would be ideal to blank the LEDs. For clean start, power the control and keep the LEDs unpowered until after sending reset followed by complete string of desired data.
It may not be possible with the boards you have, because most follow the simple approach and power the control logic locally for each pixel locally. This is reflected in the sample circuit in the data sheet.
To prevent a reset - or other blocking tasks - while a send is going on, make the reset application controlled - and delay it until after all data has been sent.
Since most neopixel products do not use the two power lines approach, you may not power the neopixels until all other things have completed the start up, then power the neopixels and send right away a reset and (blanking) data stream that you have prepared beforehand. This way you can minimize the noise moment.