They are both very cleverly put together. The Star Trek one makes very efficient use of the popular Star Trek blooper reels, plus other Trek and science fiction footage, including the rec room "jam session" with the hippies of "The Way to Eden".
STAR TREK BLOOPERS (& "THE WAY TO EDEN") VERSION
"Banned from Argo", sung by Leslie Fish; 5 min 17 sec version
And here's one featuring a slower version of the song, set to scenes from the more adult "Doctor Who" spin-off, "Torchwood":
"Banned from Argo", sung by the DeHorn Crew with Leslie Fish; 3 min 23 sec version
According to the cover of Vince Emery's "Star Trek Comedy: The Unofficial Album" LP, the DeHorn Crew also included Carol Shuttleworth, Kathleen Taylor, Robin Oye and Mary Frohman.