This site is an excellent genealogy resource and I have found it to be sound.
According to their Whitmire manuscript, The name "Whitmire" is an English spelling of an ancient German-Swiss surname. In colonial times in America the name was also recorded as Weidmayer, Whitmer, Widmayer, Widmer, Witiemeyer, Witmer, Wittmer, Wittiemeyer and Wittmeyer.
So I would look for a distant family relation with those two names. Association