I'd be very wary about doing tunes like The Old Orange Flute and/or The Wearing of the Green when there are real Irish people about (or some non-Irish British). I dare say many would forgive your ignorance for playing the "wrong" tune, but some would take grave offence. At least, that's how it was in my younger days. You wouldn't sing Eskimo Nell in front of your girlfriend's mother, would you?

Steve