Considering the vaudeville nature of the show, he probably felt like he was back in his youth.
He would have if he had spent any time on the show. 
Yes, I know that was the whole point.
Danny Kaye singing Inchworm with the cast and crew is one of my favourite memories of the show.
Avery Schreiber, as close to being a Muppet as any human.
“Inchworm” was sung twice on The Muppet Show. Charles Aznavour sung it too. In fact it originally appeared on Sesame Street. But it was written for Danny Kaye, so I guess it’s fair to say his is the definitive.