I haven't shot mine yet, but Lomographys B/W Orca film in Rodinal 1+100 stand should be a good candidate. I am currently working on a roll of their slide film in my Pocket instamatic 300, but that camera has more exposure control.
edit: That french page mentions two shutter speeds, not one or the other. Maybe plugging in a flash bar engages the slower shutter speed? You should be able to hear the diffrence.