"Death Is a Melancholy Call" in Belden may not be the same song as "William Cook," but remove the personal reference William Cook, and the content is quite similar.
Belden provides three versions, of which 'C' is in the DT, and references to others, all from the South. No music is provided.
Version A is from the ballad book of Mrs. Lida Jones, Dade Co., MO, "compiled probably in the eighties" of the 19th c., and secured by Belden in 1906.
H. M. Belden, 1940, "Ballads and Songs Collected by the Missouri Folk-Lore Society," pp. 464-465.

Both songs seem to date from the last half of the 19th c.

"The Wicked Girl," in Belden, has some of the same ideas and caution.