When was "Careless love" published? If after 1908, the melody is older. If earlier, do you think that Joseph Taylor would have had access to it? And even if so, would he have changed it from what was obviously a favourite song of his, bearing in mind his age when recorded?
I think the answer must be that the tune is older than WC Handy's song, and he may (but not must) have heard it and liked it.

Sleep easy now, Terry. Ain't you glad I came?