Learn English – What does the phrase “smiling to beat the band” mean

Found a little history on the word. It is indeed Yiddish:

shprits
spurt, to squirt, to sprinkle ∙ (m.) שפּריץ

Neal Karlen in The Story of Yiddish: How a Mish-Mosh of Languages Saved the Jews, says the word took on new meanings within a community of young Jewish comedians (exemplified by Lenny Bruce) in New York in the 1940s:

Using Yiddish as a base, the young Jewish comics helped develop only the second art form indigenous to the United States: the shpritz, a.k.a. "Jewish jazz." (African-American jazz is often thought of as the only such legitimate claimant. Curiously, "jazz" is slang for ejaculate: shpritz is Yiddish for "spray." Talk amongst yourselves.)

Wikipedia has this description from Albert Goldman of Lenny Bruce "shpritzing" during a famous Carnegie Hall concert:

Lenny worshipped the gods of Spontaneity, Candor and Free Association. He fancied himself an oral jazzman. His ideal was to walk out there like Charlie Parker, take that mike in his hand like a horn and blow, blow, blow everything that came into his head just as it came into his head with nothing censored, nothing translated, nothing mediated, until he was pure mind, pure head sending out brainwaves like radio waves into the heads of every man and woman seated in that vast hall.

Because of the word's historical association with Jewish comedy, its use in the quote you found is quite appropriate and well-chosen—even if a bit esoteric.

In the context of the lyrics I interpret it as meaning that she shouldn't be too naive and think that just being nice (smiling to people) will mean people won't try and use her. She has to be aware that other people are not always good and should look after herself because "there's a lot of bad" out there.

Of course song lyrics can often be interpreted in different ways so other people may disagree with me on this.