You have here a family tradition which is only partly true. James indeed was in the crew that took Titanic from Belfast to Southampton. He was a fireman and was aged 31.
The story about sleeping in is imaginary. If he had intended to go to New York he would have signed on with most of the crew on 6 April. If he failed to join the ship his name would be on the long list of deserters, but it isn't.
He would have returned to Belfast by taking a train to Liverpool and a ferry to Belfast.
If there is anything more about him the Ulster Folk and Transport Museum may have something from H & W records. The British National Archive has some shipping records. Somebody more expert than I am could tell you how British births, deaths and marriages records are kept. Good hunting!