From https://umgf.com/what-guitar-does-mississippi-john-hurt-play-t23461.html we have the following comprehensive reply, from contributor "Outfidel":

"For his 1928 sessions, MJH played some guitar provided by the studio. His own guitar at that time ("Black Betty", make unknown) was not considered of good enough quality for recording.

At the time he was "rediscovered" by Tom Hoskins in 1963, MJH didn't even own a guitar. When he came north to record 2 albums on the Piedmont label (Avalon Blues and Worried Blues), he borrowed Hoskins' Gibson (probably a J-45, might've been a J-50) for the recording sessions.

After his unannounced & triumphant appearance at Newport '63, the folks from the Newport Folk Festival wanted to buy him any guitar he wanted, at any price. They took him to Marc Silber's Fretted Instrument Shop at Greenwich Village, and showed him a Martin 00-42 with pearl inlays. But John was a modest guy, and he chose a simple sunburst Guild F-30 (000 size) instead. (Alas for C.F. Martin & Co. - perhaps today we would have gotten the 00-42MJH signature model?)

Most of his live performances were with the Guild, including his live Vanguard album. He occasionally played a Regal resonator as well.

For his 3 Vanguard studio albums (Today!, The Immortal MJH, and Last Sessions), he borrowed Stefan Grossman's 1930s OM-45. To my ears, these are the best-sounding of all MJH recordings. How much can be attributed to the OM-45 and how much to Patrick Sky's production, who knows?"