No such VHS like that with those songs exists unless you're referring to The Alvin Show sing along VHS tapes?
While yes I may be gone from YouTube I've started posting the albums on Vimeo. I don't know how long they'll survive but I'm willing to take the risk and test how things go: https://vimeo.com/user91364043
As someone who owns like 5 copies of The Squeakquel on DVD I can tell you that there isn't any deleted scenes unless it's only available on the Blu-Ray copies of the Film.
The Girls then later The Boys dressed as The Girls and then later all 6 together sing a parody of the Go-Go's "We Got the Beat" called "We Aim To Please". The song The Boys sing when their microphones have been tampered with, which was the song that was actually asked about in the 1st post is still as of yet unnamed.
Sorry but they've never covered that song officially.