Robert J. Menendez's The Geography of Presidential Elections also claims that Manistee County was a Hughes-Cox county, and one of only two in the country. It identifies Polk County, North Carolina, as the other one. Hughes won Polk County 52.5-47.5% in 1916, while Cox carried it 50.7-49.4% four years later. Harding did not improve that much over Hughes in North Carolina, and Cox obtained almost the same percentage there as Wilson.
Weird, Wikipedia claimed that Manistee County was the only one. Did that book give any information or reasons why the county would have voted that way? Until we find any historical evidence I think we should still assume the numbers are simply wrong. The North Carolina county is weird, but it may be explained by the massive turnout increase, and North Carolina barely swung R anyways. I would assume that one is an actual Hughes-Cox county. Are there any other Hughes-Cox counties Wikipedia missed?