The dictation cylinders are a different animal when compared to the usual " 2 minute" and " 4 minute " cylinders. Edison decided that he wasn't gong to allow compatability between the business and entertainment cylinders , so the grooves per inch and groove size were altered to attain this . The pitch of the mandrel remained the same...
Because dictation cylinders have by design, as the cylinders were designed to be shaved and reused, a smaller, more fragile groove due to wax hardening and embrittlement caused by evaporation of volatile oils and a lower level of signal by design of the acoustic recording heads used by most dictation machines of that era , I would not recommend using a dictophone to play them back.
Whatever method you decide to pursue for playback, I'd highly recommend that an electronic method would be best.