On this YouTube clip of
Tom Smith playing The Spinning Wheel on an electronic keyboard, the comment is as follows:

"A SONG BASED ON VERSE BY JOHN FRANCIS WALLER. RECORDED BY DELIA MURPHY IN 1939, WHEN I THINK THE MELODY MAY HAVE BEEN ADDED."

I am not sure how Tom Smith arrived at this conclusion but he appears to be saying that Delia Murphy used a different tune for the song than the tune referred to by J F Waller.

Delia Murphy performing The Spinning Wheel as recorded in 1939

The arpeggios are heard on that recording although I can't identify whether it is a harp or a guitar, as Arthur Daley on guitar is credited for the recording.

In my Googling earlier this morning - when the sparrows were still tucked up in their nests and my brain was not even awake yet, I did see something about Delia Murphy being the first person to set the tune to a harp accompaniment, but I am not sure whether she played an instrument, and if so, whether she played harp.

(Never do research on the internet without saving your findings because you can guarantee you will wish later that you had done so. LOL)

Ok, here it is:

Delia Murphy - artist biography

......One of her first recordings was the extraordinary "The Spinning Wheel." Written in 1899 by John Francis Waller, the song hauntingly evoked the courtship of young lovers measured by the inexorable winding of the spinner's wheel. Murphy's ethereal West Ireland brogue and Gaelic pronunciation was reinforced by a harp arrangement that was quite remarkable for the period.