Did Buddha ever say how to overcome shyness?
I would say yes, these powers include the overcoming of shyness. You are no longer meeting other people but just yourself in other guises. Also, your mind is not weaving fantasies about what people are thinking about you. Also, you have nothing to hide, no sense of superiority or inferiority and if you are sufficiently skilled no sense of personal involvement in the situation.   

Maybe a little shyness is a good thing but a Buddhist has excellent defenses against being crippled by it. A good Buddhist knows he or she is an idiot and is not surprised when others think so. I'll let you know later whether this is also true for arhats and buddhas.