It must be hard to find songs that are just right.
a lot of folk songs are dated and rural (by their nature) so the vocabulary wouldn't be much more useful than 'my postillion has been struck by lightning'.
Songs about death might be sensitive even if treated jokily as in 'She sat Neath the Lilacs' which we sang at school (in the lunchtime, unprompted by adults).
We also sang 'Once I had an old Banjo'
One-l-l-nce I ha-la-la-d an ol-l-l-ld banjo-l-l-0
I pla-la-layed it on-lo-lon my knee-li-li-li-ly
But now-le-le-ow the strin-li-lings are bro-l-l-ken so
It no-lo-lo more u-l-l-use to me-li-li-li-li-ly

I to-l-look it to the me-l-l-nders sho-l-lop
To see-l-lee what he-l-lee could doo-loo-loo-loo-loo
And now-l-l-ow the stril-lings are mended and
It's quite-l-lite as goo-l-lood as new-li-li-li-li-lew

Well, something like that anyway. Which we used to sing at secondary school (1950s, Chiswick, London), sitting on the grass making 'banjos' by cutting the edge of plantain stems with a fingernail, then pulling the leaf gently to expose the strings.