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I certainly wouldn't spray them (in containers they wouldn't dry as fast as they would in the wild and so they'd rot quickly). Usually just storing them in a cool, airy place with 'natural' temperate humidity and temperatures should be enough. You're just trying to mimic the outside world but bearing in mind that a pupa is usually located at ground level mixed in with the leaf-litter where it stays in quite stable conditions - no wide, sudden fluctuations in temperature.

Mark Shaw's rearing shed is constantly shaded by tall trees and bushes ... it has a chicken-wire door and hinged side windows (also lined with chicken wire) that can be opened all summer to let air movement through, but which also keep the rain off. The roof is painted white too - everything designed to maintain stability.

Pupae are placed in glass tubes with cork bungs and laid flat, with the collecting data in the tube so that it doesn't get lost :)

The whole process is described and illustrated in the AES publication "Rearing Parasitic Hymenoptera" by Mark Shaw (The Amateur Entomologist volume 25).