...Dance With Me, Henry...
That would be “Roll With Me, Henry”, if you listed to the ‘wrong’ radio stations.
http://www.youtube.com/watch?v=jsgBUtW_O4E
I've never heard that version of "The Wallflower/Roll With Me,Henry/Dance With Me, Henry" which you posted, but it rocks. In the original version, recorded over Thanksgiving weekend, 1954, Richard Berry sang the part of Henry. Berry is probably best known today for his 1957 hit, Louie, Louie.
Etta James answered her song with Hey! Henry, in which her boyfriend has become skilled at cutting rug.
In our home, we listened to the "right" radio stations, notably KFI, which would have played the Georgia Gibbs version of The Wallflower--which also rocks.