I don't think children nowadays will know that Dick is a diminutive of Richard.
I suppose there is a small risk of Dick Willie - but I don't think it's a big deal.
I did used to teach a child with the middle name you've chosen and the surname w i l l c o c k s. One day he came to see me in tears to say that the other children were calling him 'Willie Willie Cock' ! I had to force myself not to laugh!
Old fashioned with history:
Arthur, Albert, Alfred, Alexander, Benedict, Charles, Christopher, Daniel, David, Edward, Ferdinand, Frederick, George, Henry, Harold, John, James, Louis, Nicholas, Patrick, Phillip, Peter, Quentin, Robert, Stephen, Sebastian, Thomas