After saying I try not to discuss Irish history here goes another exception. I justify it by saying I am learning something I didn't know.Wellington never said that. In fact he was proud of his Irishness. It was said about him by Parnell, who hated Wellington's guts.
It seems it was O Connell who said it about him, according to the IT that repository of all truth. https://www.irishtimes.com/life-and-style/a-bit-of-welly-the-iron-duke-s-irishness-1.1546456
I hadn't realised that it was said about him rather than something he said himself.
However he does illustrate the point that he was of a class who, despite generations in Ireland still sent their sons to school in England.
You say he was proud of his Irishness, have you any reference as to that or what it meant to him to be Irish.