That clip might also be from "The Pat Boone Chevy Showroom" which ran from 1957 to 1960. I think Woody Allen was a staff writer on that show.
Anyway, the closest guess I have (if the clip is from the late 50's to early/mid 60's) would be Dee Clark.
The singer in the video might've been a bit older than Clark would've been at that time, though.