"How old may she be,
Billy Boy, Billy Boy?
How old may she be,
Charming Billy?
Three times six and four times seven,
Twenty eight and eleven,
She's a young thing,
And cannot leave her mother."
This, despite the questionable math, puts the refrain into a very ironic context.
My understanding of square dance singing calls is that many of them were set to popular music of the time (though I have no idea about this particular one). So if your audience was expected to know this song and the context behind the refrain, that would be one thing. Notably, though, the square dance-edited version is missing this context, and it adds the line "Promenade this pretty thing, won't you help me to sing" to the refrain, "She's a young thing, And cannot leave her mother"! So it'd be quite something else to hear this line on its own, which makes it sound like you should be promenading with your underage partners/corners.
There's no universal answer to "is this acceptable" because it depends on your "contra dance crowd" who is doing the accepting - this can vary widely between dances, even within the same city. You'll have to figure out if the dancers are ok with it as is, might be ok with it if you give them some background about the song before you do the walkthrough, or would not be ok even with that. However, I think you'll find a lot of other material is less objectionable to any audience (and you already have some intuition for this, since you asked the callers list about this one).