The "-ker" connection is real, not apparent. Back in the early days, the word Shaker was coined as a contraction of Shaking Quaker (referring to the Shaker's dancing).

Which reminds me--the U.S. Attorney General at the time of the Haymarket Massacre (I forget his name) liked to be referred to as "The Fighting Quaker". Popularly, though, this became "The Quaking Fighter".