Tam Murray, 40 and Murdo Morrison, 23 remain missing after their vessel disappeared off Lewis and the body of crewmate Douglas Craigie was found at sea.
In 1965, his remains were exhumed and brought to Glasnevin Cemetery, Dublin. But a commemoration society in his name, who have lodged the application, has said it wants to "fulfil his wish" to be buried in County Antrim.