I'd love to help, but I don't have the recording.

It seems there are several different songs called SOLDIER'S FAREWELL. Any idea where Dessie O'Halloran got his?

I searched with Google using several phrases from the lyrics that have been posted so far, and came up with nothing.

The Bodleian Library has these, but I suspect none of them is the right song:

THE SOLDIER'S FAREWELL, OR, HEAVEN DEFEND THE RIGHT
("Farewell, farewell, old England ...")

THE SOLDIER'S FAREWELL ON GOING TO THE WAR
("Farewell, farewell, old England! ...")

THE SOLDIER'S FAREWELL TO MANCHESTER
("In coming down to Manchester to gain my liberty ...")

THE ASHANTEE WAR; OR, SOLDIER'S FAREWELL
("Oh sister I must soon be going ...")