Here's what makes it match your description:
* Opera-like Tune: The song's opening is indeed reminiscent of a classical opera, particularly with its strong use of melody and harmony. It shares similarities with the style of Mozart's "The Marriage of Figaro," even if it's not an exact copy.
* Character Names: The song features a verse that lists various Cartoon Network characters.
* Airing Period: Your timeframe of 1994-1996 falls right within the song's original run.
While the song isn't a direct adaptation of Figaro, its operatic style and character-naming verse strongly suggest it's the one you're looking for.
Do you remember any specific lines or character names mentioned in the song? That could help confirm if this is the right one.