Cochrane in my family tree, but from Kilmarnoch a William Cochrane of Low glencairn Street who married Isabella Lamberton of West Muir July 4 1850 at Bogside, their first child was David Lanesborough born in Kilmarnoch then they went to Australia then on to New Zealand and settled in the south Island and added another eleven children to their family, so not sure whether connectd to your Edinburgh Cochranes
Cheers