The collector Richard Runciman Terry wrote that "English seamen usually pronounced it 'Shannandore.'" (I.e., "Shannandaw.")

"Shannadaw" must also have been sung, since one printed version is called "Oceanida."   

Either way the "r" might or might not have appeared before a vowel like "I."

The usual U.S. pronunciation of the valley, river, county, and town is "Shen-an-do-ah."

But that's a poorer fit for the meter in any case.