Worth noting that this is more difficult than a similar surgery would be on a mammal because chickens, like all birds, don't actually have a larynx--what we normally mean by "voicebox." Instead, they have two syrinxes, one on each side of the bifurcation as the single larynx splits to reach each of the lungs. Instead of one pair of vocal folds to remove, you'd have two, and of course you'd also be trying not to damage the fragile air sacs as well as the much closer lungs while you're at it.
You can see some of the respiratory anatomy over here on this songbird diagram. (Incidentally, note that birds also don't have a diaphragm either--that's a mammal thing.)
As far as I can tell from a cursory search, rather than outright removing the synringes the usual "decrowing" surgery is to simply cut an incision into the syrinx so that air can't be forced to vibrate through the folds as effectively: instead, it hisses into the nearest (clavicular) air sac. Ideally. Assuming:
a) that the slit on either syrinx doesn't heal shut, either partially or fully
b) that you don't nick anything else important while you're in there
c) that the anesthesia doesn't just outright kill the bird--birds being generally more sensitive to general anesthesia and related complications
There's
another thread here with a member who did this surgery on several roosters; results seem mixed.
