The cable was indeed laid by having two boats meet in the middle of the ocean, although it took several attempts. See http://en.wikipedia.org/wiki/Transatlantic_telegraph_cable#Transatlantic
While that article does not mention Peter Cooper, this was taken from his wikipedia page. "In 1854, Cooper was one of five men who met at the house of Cyrus West Field and formed the New York, Newfoundland and London Telegraph Company. He was among those supervising the laying of the first Transatlantic telegraph cable in 1858."