Since this seems to be more of a missing ingredient issue than a substitute for dietary reasons, I would recommend adding a tablespoon of melted butter to the mix to add the fat missing from the milk. Water will work just fine. It is the fat from the milk which adds the taste.
You can add water in place of milk in your Jiffy corn muffin mix, but your corn bread won't taste as good. The most workable option is using an egg substitute and non-dairy milk if you can't use milk at all.