But it it’s hardly an odd use of the word, just a less usual one.
Right. Like many words of its kind, the leap from minutia to “mincing words” is interesting.
Anyway, regarding “Oh, Snap” itself, Wikipedia has a short paragraph (without citation) that notes that rap artist Biz Markie (Marcel Hall) popularized the phrase in 1989:
Oh, snap! is an expression popularized by Markie in the 1989 song “Just a Friend”. It has since entered the mainstream as an expression of disbelief. The phrase is a polite substitution for “Oh, shit!” It has also entered use as acknowledgement of a diss by third parties, to heighten the feeling of disrespect and insult. “Oh, Snap!” has been known to be used as another way of saying “zing!” It may also be used as an expression of shock or amazement.[