Born in Manchester on 25 April 1916, he grew up in Levenshulme Methodist Church. He left school at 14, heard the call to preach at 16 and was accepted for the ministry in 1938. He spent two years at Handsworth College, followed by a year at Headingley College, before being stationed in Port Isaac. His wife, Joan, was a seventh-generation Cornish Methodist and the rest of his ministry was spent mainly in Cornwall. He became the acknowledged expert on Cornish Methodism and was a founder member of the Cornish Methodist Historical Association, formed in 1960, serving as the editor of its Journal until 1996 and then as President. The extensive 'Shaw Collection' of printed and manuscript material on Cornish Methodism is now in the Courtney Library of the Royal Institution of Cornwall at Truro.
He was Secretary of the Cornwall Council of Churches from 1971 to 1978. He played a leading role in the development of Gwennap Pit as a place of pilgrimage and tourist attraction, and of the nearby museum at Wesley Church, Carharrack. A longstanding member of the Wesley Historical Society, he was its General Secretary 1961-1981 and British Secretary of the International Methodist Historical Society. His books include the Wesley Historical Society lecture for 1965, on The Bible Christians 1815-1907, A History of Cornish Methodism (1967) and A Methodist Guide to Cornwall (1991), as well as numerous local histories. In 1961 he was made a bard of the Cornish Gorsedd. He retired in 1981 and died at Perranporth on Wesley Day, 24 May 2001.
His wife Joan Hellyar, née Menhinick (1922-2012) was Cornish by birth and was educated West Cornwall School, Penzance. She trained as a primary school teacher at Gypsy Hill training college. She was very much involved in voluntary organisations in the community as well as in Sunday School and youth work in the Church. She shared in her husband's active interest in Cornish Methodist history, notably in the development of Gwennap Pit as a heritage site.