Well, following on from my previous post, out of the set list you posted, "The Leaving of Liverpool" and "The Gypsy Rover" are both unlikely to be Irish.

I appreciate that "Gypsy Rover" was copyrighted by an Irishman in the 50s, but I believe most of the evidence points to it as having Scottish origins, with the 1950s version being a very close adaptation of a much older song.

"Leaving of Liverpool" has often been claimed as a "song of Irish emigration" but if you look at the words it's clearly a song about a sailor who's done several long voyages before. He knows Liverpool well, from the locations he mentions and indicates that it'll be a long time until he sees his girl again, not "never" (ie, he's expecting to come back to Liverpool in the future). So the balance of probabilities is that this is an English sea-song, rather than an Irish emigration song.