It's 'daddy' in the jazz-slang sense of 'wealthy boyfriend' - which never really caught on in Europe but which crops up a lot in this genre. Not that the jazz-slang sense of the word is particularly commendable in feminist terms, but one of the joys of slang is that it doesn't give a flying one about etiquette. I still cannot imagine how they got away with that 'Finnan haddy' line.
On the 'daddy' theme, for a wonderfully inexcusable song which, even at the time, pretty much kicked feminism in the shins, check this out.
But to get back to A-Ha - I hated them when they were in the charts, because they were sold as popstar pretty boys. But every time I hear them now, I think, "That's unexpectedly good stuff." 7/10
At the other end of a writing career, here's a proper grown-up composition with a proper grown-up theme - a song that addresses something other than being twenty-three and horny. (Not that there's anything wrong with that, George.)

