Actually, bread flour is often labeled regular flour. The option is pastry flour (called cake flour if it is white). Your cookies should be fine, they are one of those foods unaffected by protein content (gluten is a protein that develops into long strings with kneading that give bread good texture). Pastry flour helps keep the crumbly texture in high fat products like shortbread and pie dough. White or whole grain "bread flour" will not affect the texture of your cookies.
Besides, ingredients are seldom what makes a cookie disaster--someone will eat your mistakes as quickly as they will your best offering., get baking girl.
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