I don't bother with the old abc-reading programs I used to use any more, except for their indexing functions; the online facility is better, at least while I have an "always on" connection.

I suspect that the Babes in the Woods tune you know derives from the 19th century William Gardiner song based on the old story. The Coppers, for example, have a "processed" form of it (with the melody improved, to my ear). You can see Gardiner's song at The Lester Levy Sheet Music Collection:

Sweet Babes in the Wood. A Ballad. Founded on the well known Legend. Philadelphia: B. Carr's Musical Repository, n.d.