Welles could be pretty hard to track down, according to many people that knew him. Maybe Horowitz figured that Houseman was the next best thing.
Here's the end of the play:
which transcribes as:
"...or in bed or in any sort of ordinary or maybe embarrassing position, the bomb will explode - quite silently - and you will be left with - let's say - a piece of soap in your hand, or a toothbrush in your mouth. You won't remember what a toothbrush is, or how to remove it. The face in the mirror's will be a stranger, the face of somebody you'll never get to know - not even by name. Don't say you weren't warned...
(He starts away, then stops for a last word -)
Of course, you realize (since this is old stuff) that what you must do is organize a conspiracy - a world-wide conspiracy - to overthrow, not your government, or any other government, but the sovereignty of your nation. All our nations. ?????? is wishing you, good night.
(He blows out his lamp. When the lights come on again, the curtain is down and the play is over)"