Shaw was born in Halifax in West Yorkshire, the son of James Shaw, a dyehouse labourer, who worked at a local mill. When he was 13, he was started work as a labourer in a cloth mill. He became apprenticed to a wire drawer, but the low wages on offer were not attractive and he soon took a series unskilled jobs in local engineering works. He was thus well placed to join his father in a new business repairing small machine tools used in munitions production during World War 1. After his father's death in 1929 he started his own small business as a road contractor.
In 1934, he patented his invention (patent No. 436,290 and 457,536), based on the 1927 reflecting lens patent of Richard Hollins Murray. A year later, Reflecting Roadstuds Ltd was formed to manufacture the devices. The wartime blackout gave a huge boost to production and the firm, located in Boothtown, grew in size making more than a million roadstuds a year, which were exported all over the world. They are now replaced on many roads by reflective plastic. Such a success was the invention of the "cat's eye" that in 1965 he was rewarded with an OBE for services to exports.
He never married and he died on 1 September, 1976 at Boothtown Mansion, Halifax, where he had lived for all but two of his 86 years.
In 2005, he was listed as one of the 50 greatest Yorkshire people in a book by Bernard Ingham