From context, cherry seems to be a typo for chary:
4.a. Careful, cautious, circumspect, wary.
6. Careful not to waste or part with, frugal, sparing (of).
Source: Oxford English
Five Jaunt attendants circulate, speaking in low, careful voices and offering glasses of milk.
The Jaunt, being first published in The Twilight Zone Magazine in 1981 (Wikipedia — The Jaunt), may have been put through a magazine editor who either didn’t correct King, or over-corrected him.
You can hear the pronunciation of chary — which sounds just like cherry — at Cambridge Dictionary — How to pronounce chary.