http://www.dailyhalacha.com/m/halacha.aspx?id=595 Chacham Ovadia would permit you to close the fridge with a shinui. All other poskim would not.
If you need the food in the fridge and there's no way to take it out b/c it will spoil, then just leave the fridge slightly open.
If that will cause the food to spoil, then you can use a goy to (repeatedly) open and close the fridge for you.