I need to make hard sugar cookie icing without corn syrup?!

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powdered sugar, vanilla and a little water,using enough powdered sugar to get to desired thickness and you are good to go.
I dont care to use egg white due to salmonella threat.
What keeps frosting from getting hard is putting any kind of fat in it, like butter.
I have never used corn syrup in any icing so not familiar with that method.

Cookie cutter sugar cookies

Ingredients
2 cups flour
1 1/2 teaspoons baking powder
1/4 teaspoon salt
6 tablespoons unsalted butter
1/3 cup vegetable shortening
3/4 cup sugar
1 egg
1 tablespoon whole milk
1 1/2 teaspoons pure vanilla extract

Method
Preheat oven to 350°. Line a cookie sheet with parchment paper.
Stir together flour, baking powder and salt. In a large mixer bowl beat butter until butter is softened.

Add sugar and beat until fluffy add egg milk and vanilla and beat well. Add flour mixture and beat until well mixed. Divide dough in half. Cover and chill at least 3 hours or until easy to handle. Roll dough 1/8 inch thick. Cut with your favorite cookie cutters. Place on cookie sheet and 7 to 8 minutes. Remove from oven. Cool on pan 5 minutes. Remove to cooling racks and let cool completely before frosting, if desired.

Makes 36 to 48 cookies.

Creamy Icing
In a small bowl beat 1 egg white, 2 teaspoons lemon juice or vanilla. and enough powdered sugar [1 1/2 2 cups] to make icing of piping consistency. Spread icing on cookies, let dry. If desired, add a drop or two of food coloring, spoon into a zipper style plastic bag, forcing the icing to the corner. Make a small hole in the corner and use to pipe decorations onto cookies.

This free 88 page pdf on cooking mastery may help you.

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