Hi Piers,
The only thing that comes up in my mind is that "pai pai" in Hokkien could (and does) mean "a praying gesture". So, if you stand in front of the statue of a god in a temple, and bring your hands together in front of your face or chest (or anywhere in between), palms pressed together, and you gently "shake" or "wave" your hands vertically several times in a "praying gesture", then you are doing a "pai pai". This is with an unaspirated "p-", which is close to a Mandarin "b-" (in pinyin).
It is conceivable (but a bit far-fetched?) that such a waving motion could be borrowed to mean a "fanning" action, and thereafter transferred to the noun itself.
[I say "far-fetched" because "pai-pai" is a "vertical" motion, whereas fanning is usually a "horizontal" motion. Even when fanning is a vertical motion, it's "perpendicular" to the flat-axis of the hand (in prayer), whereas "pai-pai" is "parallel" to the flat-axis of the hand.Hope that makes sense - these motion and direction things are very hard to describe in words!]