(The) or Choking-stool, for ducking scolds, is not connected with choke (to stifle), but the French choquer; hence the archaic verb cuck (to throw), and one still in use, chuck (chuck-farthing). The cucking-stool is the stool which is chucked or thrown into the water.
Now, if one cucking-stool was for each scold, Some towns, I fear, would not their numbers hold.
Poor Robin (1746).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894