Annoying stepper's sound

You can use these to dampen the sound and vibrations, i use plenty of those.
www.ebay.com/sch/i.html?_from=R40&_trksi...otor+Damper&_sacat=0

www.3dp2go.com/stepper-motor-damper-for-...per-motor-p-343.html

They will not totally remove the noise and vibrations, but they will make everything a lot quieter and more pleasing to the ear.

That is the noise produced by the drive PWM current limiting so here are some tips:
Try a different power supply, cheap power supplies produce way to much ripple.
Adding 220 to 470uf capacitors directly to each drives power terminals should lower or completely get rid of that noise.
As a side note, the TB6xxx series drives will need also some 0.1 to 0.47 uf capacitors in parallel with power supply, or even betteter said capacitor should be added inside the drives connected between ground and the "VRef" input to IC.

Opening the drives is a last resort, you have plenty to test with without opening them. Do test at the exact order i wrote them above. Chances are you will get satisfying results before reaching the "open the drive" point.
Opening them would require good knowledge of electronic and schematics and soldering skills, or the magic smoke will escape from them !
Anyway you decide to go, i will be here to help, just do not hope you will completely get rid of it, you won't.
FYI, i never did try to remove that noise, i just like it and it reminds me that one of machines in ON. I can hear even some connected to some high tech stepper drives made by LAM Technologies, as they are de facto the best drives i had in my lifetime. I have used plenty of the DS series, have a look
www.lamtechnologies.com/Resources/Doc/DS10_BRUK.pdf

I do not have the schematics, so pictures would be nice, although not very helpful.
You do need that for any modification to it. Interesting to see a PIC , as the better drives use DSP processors for managing micro stepping. Anyway, it looks like the only option for now is just adding 0.1 to 0.47 uf capacitors to power rails if they already do not have them.