In our neck of the woods, we would consider only the following to be essential:
Black Velvet Band
Fields of Athenry
That would be the only time we would want to do these. Normally we only sing the Wild Rover to one of the many 'wrong' tunes it fits (The Boxer, The Laughing Policeman, Supercalifragalistic...)
Anything else that sounds reasonably authentic will usually suit. With a know-nowt pub crowd, it useless trying to be subtle. They don't know that The Banks of the Bann is Irish. So fast tunes, and comic songs are favourite. We try to avoid anything too political, someone (usually the landlord) will object.
Murray Macleod - I like songs mixed with tunes. My own contribution to this genre (Pretentious? Moi?) is Spanish Lady, sung slower than usual, mixed with the A part of Christmas Eve, then up to speed at the end with all three parts.