Well, that is an interesting name so if it was in the Mayflower book we must be talking about the same family you would think.
It is on Pg. 79, that 2 Shiverick's are mentioned.
A Nathaniel Weeks (Edward, Capt. Matthew, Elizabeth, Mary) m. Margaret Shiverick in 1701/2 in Falmouth, MA. The author believed she was the daughter of Rev. Samuel Shiverick of Rochester and Falmouth. The Rev. was a Huguenot.