Despite me being born in 2000. I could've sworn I saw the infamous Wegman Dogs sketches as a kid. By my surprise they stopped making those creepy dogs-with-human-hands clips circa 1990's.
Do you have older siblings? Maybe you watched a recording of a Sesame Street episode from an era when they still showed these segments.
I remember seeing them on TV in maybe 2006-2007. I think they just kept showing them in the current episodes to fill time.