Possibly on Nick, Maybe a special/episode. Anyone know?

Nope, but thanks for the suggestion.
He recalled them singing like "Our Paradise, USA!" (pronounced as Yoo Ah Sah of course)

I believe the movie you're thinking of is "Globehunters: An Around the World in 80 Days Adventure", and it was a TV movie on Nickelodeon that was part of the "Nickelodeon Sunday Movie Toons" which were a series of animated movies that Nick aired around 2003 on Sunday afternoons and were all based on classic, public domain stories but with new takes on them.

Most people on the LMW know of this movie series for one of it's movies in particular, being The Electric Piper, and while TEP was the one I remember the most, I remembered everything about this one but the name until recently. The others I remembered were a (very loose) adaptation of The Time Machine called "Time Kid", and an adaptation of Treasure Island that used similar transitions to Liberty's Kids. I think there were others, but those four were the only ones I remember.

No, but the guy who made RSK did make a version of the Lost World called like Dinosaur Island or something. As far as I know maybe he did throw together a Treasure Island version too.