Harris and the Mare, unaccompanied? I'd love to, but I don't see how. There's that long silence between lines 2 and 3 of each verse (by which I mean, in the accompanied versions I've heard, there's that long stretch with no singing). It has always seemed to me that that puts the song out of bounds for a single unaccompanied singer. What am I overlooking?

In answer to your question, that pauses can be very effective in unaccompanied singing, just don't do it every verse, but use them where you need to create tension or to provide a natural break in the story. Remember that as well as singing a song you are telling a story and you need to feel the flow of the story as much as the rhythm of the song's melody.