I don't know of anything that cures instantly and you can smell super glue after it dries, that is the out gassing. Also different materials such as plastic, will stop out gassing at a certain temp, but then out gas when the temp is raised. With that said chances are the out gassing from a small amount of glue isn't going to have any effect on your animal, but if you want to be paranoid, put it any an environment warmer than the one it will be used in, wait for it to stop out gassing, no worries.