Why can you not refrigerate the dough? We have never thought of sugar cookie dough as being so delicate that it can't enjoy a little downtime in the refrigerator. For that matter, most sugar cookie recipes want you to refrigerate the dough to make it easier to roll out. No, you cannot let cookie dough with a raw egg mixed in sit out at room temperature for 36 hours. We are generally less strict than the US Department of Agriculture when it comes to bossing you around, but in this case we're putting our foot down.

Should you wish, in the interest of self-preservation, to scrap your recipe, you might like to consider one of these as a replacement: