For the record - We used the "I'm a Little Dutch Girl" song as a skipping rhyme in Melbourne Australia in the 1950s. We ended it with:
Boy: Here is your hankie etc.(in place of ribbon)
Girl: Come back I love you etc.

The tune we used was "Ach Du Lieber Augustin".

The tune I learned from an elderly Englishman for "Poor Jenny Lies a-Weeping" uses the same phrasing but the notes are different. You can sing both tunes together with an interesting effect.
                                     Cheers, Joy