How did men cover up their beards if they played women’s roles in Shakespeare’s theater?
Usually boys played women’s parts on stage, so there was no problem about beards. In fact, Hamlet jokes with one of the actors who visit the court in Denmark: “Why, thy face is valanced since I saw thee last,” meaning that the boy has reached puberty and started to grow a beard. Since his voice would change about the same time (Hamlet says, “Pray God your voice, like a piece of uncurrent gold, be not cracked within the ring.”), that would signal the end of female roles for him. Older men probably played female roles from time-to-time, such as comic figures like Juliet’s Nurse. In that case, they would probably shave off any beard.