It has been claimed that the traditional Japanese umbrella, made of slender bamboo and rice paper and easily breakable, could, when held by a man, symbolize the small size or weakness of his organ. However, there is not a single instance in our collection of a man holding an umbrella who appears particularly feeble.
While some men who are shown spying on others and masturbating do hold an umbrella (Fig.2.), a possible indication of weakness, there are equally other men who are masturbating, but without umbrellas.
Source: ‘Japanese Erotic Art: The Hidden World of Shunga‘ by Ofer Shagan