Daniel Cassidy, in his infantile work of pseudo-scholarship, How The Irish Invented Slang, claimed that the word ‘pud’, a slang term for penis, derives from the Irish word bod, with the same meaning.
If pud had no meaning in English, this would be a reasonable enough claim. However, pud does have a meaning in English. It is a common shortened form of pudding, which is on record as having been used as a slang term for a penis in British English as early as 1719. Several types of sausage commonly eaten in Ireland are called puddings – black pudding (putóg dhubh) and white pudding (putóg bhán or drisín).
There is absolutely no sensible reason to suppose that pud is anything but English.