Most of the deicers are alcohol based, with some form of glycol- as far as I know. Definitely check the warning label. I'd expect that most of the warnings would involve ingesting, inhaling, or getting it in your eyes. But, do check!
I'm not certain what makes the blue color you have on your hands. Hopefully it's just a dye that allows you to see where it's been sprayed. The various alcohols etc should evaporate pretty fast and not cause you much harm in a home use situation. (rather than constant industrial use on a daily basis.)
Try using oil or lotion with water (instead of soap), along with a scrubber to get the color off of your skin.
Source: I use a lot of chemicals (when NOT pregnant!) for some of my furniture and "art" projects. Husband is biotech engineer.
Hope that helps!! Also... maybe have somebody else de-ice for you in the meantime. ;-)