Would carbonated water be a good substitute for two eggs in this cherry loaf recipe? I would like to replace the two eggs in this recipe with carbonated water:

Ingredients

1/3 cup shortening, butter, or margarine
¾ cup granulated sugar
¼ cup brown sugar, lightly packed
2 large eggs, room temperature
2/3 cup milk, room temperature
1½ tbsp orange juice, room temperature
2½ tbsp maraschino cherry juice, room temperature
1 tsp vanilla
¼ tsp almond flavouring
2¼ cups all-purpose flour
2 tsp baking powder
¼ tsp baking soda
¼ tsp salt
¾ cup maraschino cherries, well-drained, blotted dry, and coarsely chopped

Is carbonated water a good substitute for this? If it is, how much should I use to replace two eggs? Or does anyone have any suggestions of what I should use instead?
It would be useful to see the whole recipe, but the answer is probably no. Egg whites are protein and water, and yolks are fat, protein, and water, and each contributes important things to cakes. There is complicated chemistry going on, and you can't just eliminate the eggs from a recipe like this. Carbonation does nothing. However, if your recipe calls for, e.g., whipping the whites to create a stable foam, you could replace this with whipped aquafaba. There are other similar vegan substitutions that could be made depending on how your recipe is using the egg.