Hi, Saul! While sugar definitely acts as a preservative, cookies left out in the air will typically go stale long before they become moldy. Freezing is the best way to keep cookies for future use. Cookies don't typically have much liquid in them, so substituting applesauce for sugar will have a significant impact on the texture of the resulting bake. But you can feel free to experiment with replacing the eggs with applesauce instead and then reducing the sugar, as both contain a large percentage of water. Happy baking! 

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