"I tried for a lamp or a Spanish shawl or a golden filigree...."
Much more creatively specific than what I'd expect from any 19th century broadside. And I know what "filigree" is, but what's "a" filigree if not something self-consciously poetic? And all three items seem (to me)rather lavish for a 19th century funfair, even if made impossible to win.
"I took my chance and I won that girl." The light-hearted puns on "taking a chance" and "winning" the girl seem most appropriate to a modern music-hall or even a Broadway song.
Certainly one could give a wheel a "whirl" since the 16th century, but the implied pun on "give it a whirl," i.e., "give it a try," is something else that sounds very modern. The OED's first example is from 1884, but the sources are all American (except for one from P. G. Wodehouse, who loved to use Americanisms) until the 1960s.
Trad lips can be "red," but I'm not sure that they're ever "soft."
What are the odds that any genuinely old song would bring together *all* of these unlikely or seemingly anachronistic features in three stanzas and a refrain?