hello and welcome to HCM,
Throat making a loud sound during swallowing can be due to many causes but most of the time it is nothing to be worried about. The relation of vocal cords or the organ of voice box is also not an issue here.
However you may evaluate yourself by performing an upper GI endoscopy
to rule out any major problem which can cause such sounds to emanate from the throat.
Also try not to drink large quantity of liquids at a time and take short or small sips which can reduce the sounds.
take care and do not worry so much about a sound during swallowing when swallowing itself is fine
Dr Sriram Nathan