Lol I remember hearing it when I was a kid and thinking "whaaaaat?" And on Nickelodeon whenever one of the presenters used to reference it or song it they never mentioned the word fanny and would always say "Shake your whammy funky song". I always thought it was such a rude song :D
When I first heard it on Nickelodeon, I don't think I realized what they were saying, or it didn't sink in. I might have either thought they were saying "thang" (basically "thing" with an accent), or it just never registered they were saying fanny, for whatever reason (either not knowing what it meant in the UK, or just not noticing it.)
It wasn't until they aired Sabrina on CITV, or some other channel, and they edited out the "fanny", and made Funky Song sound really weird, and I couldn't work out why they were editing it.
I didn't know what "fanny" meant when I was a kid so it was just a song but now, I realise woah. Same with full stop and period. In Year 7 when we were told about the American word for full stop we laughed.