This is a late response to the question, but I believe that it is Harry Morgan who sings in "Look Out Broadway." The voice sounds convincingly like Harry Morgan's, and unfortunately to disagree with you, his part isn't well sung. (Earlier in the movie it was even suggested that he couldn't sing, in a scene when he did a run-through the song "Frankie and Johnnie.") The assumption that Harry Morgan does his own singing is also because the two women's voices (Donna Douglas and Audrey Christie) are excellent, and probably dubbed by others (though I have no reason to know that both weren't excellent singers). The soundtrack credits at IMDB show the song as "performed and sung by Elvis Presley, Eileen Wilson, and Ray Walker." I can make no sense of that, unless those were the names of two actual vocalists, apart from EP, and even then, one member of the quartet is omitted.
I'd be happy to be enlightened. I like that song, as well as most of the music in this movie. It would be a credit to the two actresses in that song if they actually sang it, and I've always enjoyed Harry Morgan as a non-singing actor, so he gets a pass.
Ray Walker probably a member of El's Jordanaires;