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According to my personal experience, no much damage to DNA is done if you keep specimen for one day in your collection kit. Yes of course after returning to the lab one should keep them at zero degrees or minus twenty. Immediate killing is important so that fluttering of wings won't damage the wings which in worse case might affect the identification.
So I suggest you to go for any physical method to kill the specimen instead of taking dry ice along with you in the field causing inconvenience.
Thank you for that advice.