Not sure who did the voices…maybe some of the novice puppeteers of the time (Marty Robinson, Brian Meehl, Kevin Clash, David Rudman, etc) did the voices and then the tracks were sped up, but that's just a guess. It could have been Fran, Jerry, Frank, Jim, and Richard for all we know.
My favorite part is the ending when Cookie Monster flips out at the sight of the cookies and then runs out the door in terror. It's so uncharacteristic of him, but so hilarious at the same time. Especially when he comes back and eats the cookies like the monster we all know and love.