“The cast came from a specific Star Trek episode.”
Unsupported
Correction
No source names one.
Shatner said only that the cast was made "so that I wouldn't have to be available for the prosthetics that they'd put on my face to look old or evil." Any episode title attached to the story is a guess, and the competing account puts the cast in The Devil's Rain, not Star Trek at all.
Sources 1
What people actually said
“They made a mask of my face on Star Trek so that I wouldn't have to be available for the prosthetics that they'd put on my face to look old or evil.”