There are no credible sources to verify Swami Vivekananda's explanation on why Indian women don't shake hands.
Several websites have published that once a British man had asked Swami Vivekananda why Indian women do not shake hands. Responding to that man, Swami politely asked whether it’s okay to shake hands with the Queen of Great Britain. The man replied, no. So, Swami Vivekananda said that ‘we treat all women in India as queens’.
However, there is no official source to confirm the same. Therefore, the claim is unverifiable.