I make no claim on the possible telegraph engineer connection, as I do not know this Cookes background.
Here is a brief part of the telegraph engineers bio - just to give some dates. It makes no mention of connections to quarries, explosives,railways (apart from telegraphs) or North Wales.
WILLIAM Fothergill Cooke was born near Ealing on May 4, 1806, and was a son of Dr. William Cooke, a doctor of medicine, and professor of anatomy at the University of Durham. The boy was educated at a school in Durham, and at the University of Edinburgh. In 1826 he joined the East India Army, and held several staff appointments.
In 1833-4 he studied anatomy and physiology in Paris, In summer of 1835, while touring in Switzerland
As the Cooke and Wheatstone apparatus became perfected, Cooke was busy with schemes for its introduction. Their joint patent is dated June 12, 1837
In 1845, the Electric Telegraph Company, the pioneer association of its kind, was started, and Mr. Cooke became a director.
His latter years were spent in seclusion, and he died at Farnham on June 25th, 1879. Outside of telegraphic circles his name had become well-nigh forgotten.