I think "handsome" in this instance means "generous" or "nobly acting" as in "Handsome is as handsome does."

In all the information here (including the old thread) I don't think I've seen the other verse that I know, which fits very neatly betwen the standard first verse ("I wish I was...") and the usual last verse ("Now, in Kilkenny..."). I learned this in the 1960s, and I'm not sure where. I think it was something the late Stan Arthur had typed out, but where he found it I don't know.

I lay me down here, beside the water,
Alone I'll rest me in my grief and woe,
Anf if there's no-one who will assist me,
Throughout this country I alone must go.
I'll go a-roving all through this nation,
Through Meath and Connaught and County Down,
Through Clare and Mayo to the County Wexford,
Ah, but I'm weary now, so i'll lay me down.