Humans can speak without using their vocal chords; it's called whispering.

Technical note: sounds produced without vocal chord vibration are called unvoiced. In English, the sounds /p/, /t/, /k/, /f/ and /s/ (and others) are unvoiced; the major difference between them and their voiced counterparts /b/, /d/, /g/, /v/ and /z/ is that the vocal chords vibrate for the voiced sounds. When whispering, the vocal chords don't vibrate, and all sounds are pronounced unvoiced. Try it yourself: whisper "bid" and "pit", "zit" and "sit" and try to hear a difference.

(Whispering is not normal speaking at a low volume. It's specifically speaking without vocal chord vibration. One can speak normally at a low volume, but that's not whispering.)

Humans without vocal chords are not mute; they just cannot speak loud.

The standard medieval way of ensuring that a slave could not speak was to cut their tongue. They were quite good at it, and were perfectly able to cut a person's tongue with very little risk of killing them.

Mute slaves, that is, slaves with their tongues cut, were pretty common, especially in the Ottoman Empire. The goal being that, of course, they wouldn't be able to reveal secrets. (It didn't actually work.) Mute executioners were also not uncommon, also especially in the Ottoman Empire.

I've never heard of mute soldiers.

In western Eruope it was not uncommon for monks to take vows of silence. No need for surgery when devotion can work as well.

Humans can make noise without using their phonation apparatus, for example by clapping their hands.

Humans can speak without using their vocal chords; it's called whispering.

Technical note: sounds produced without vocal chord vibration are called unvoiced. In English, the sounds /p/, /t/, /k/, /f/ and /s/ (and others) are unvoiced; the major difference between them and their voiced counterparts /b/, /d/, /g/, /v/ and /z/ is that the vocal chords vibrate for the voiced sounds. When whispering, the vocal chords don't vibrate, and all sounds are pronounced unvoiced. Try it yourself: whisper "bid" and "pit", "zit" and "sit" and try to hear a difference.

(Whispering is not normal speaking at a low volume. It's specifically speaking without vocal chord vibration. One can speak normally at a low volume, but that's not whispering.)

Humans without vocal chords are not mute; they just cannot speak loud.

The standard medieval way of ensuring that a slave could not speak was to cut their tongue. They were quite good at it, and were perfectly able to cut a person's tongue with very little risk of killing them.

Mute slaves, that is, slaves with their tongues cut, were pretty common, especially in the Ottoman Empire. The goal being that, of course, they wouldn't be able to reveal secrets. (It didn't actually work.) Mute executioners were also not uncommon, also especially in the Ottoman Empire.

I've never heard of mute soldiers.

In western Europe it was not uncommon for monks to take vows of silence. No need for surgery when devotion can work as well.

Humans can make noise without using their phonation apparatus, for example by clapping their hands.