Looks like pop/rock is covered.
For country, Johnny Cash. The first person elected to both the Rock and Roll and Country Hall-of-Fame—and it sure wasn’t for his singing or guitar playing. Folsum Prison Blues, I Walk the Line, Wanted Man (with Bob Dylan), I Still Miss Someone.
For blues, Muddy Waters. His song-writing and guitar playing influenced Cuck Berry, Eric Clapton, Jimi Hendrix, SR Vaughn, Bob Dylan, the Rolling Stones (named their band after one of his songs) and many others. I Can’t be Satisfied, Rolling and Tumbling, Rolling Stone, 32-20 Blues, Mannish Boy.