The winder II will work on all three RZ67 models, the winder I will only work on the first RZ, so either model will be fine for your camera. The winder II also has an input for an external power source, if that's important. I haven't used it much, so I can't say how long a set of batteries will last.
I just tested it, yes, the winder will cock the shutter/mirror without advancing the film if the lever is set to "m". There's a bit of vibration from the winder but it's definitely less clunky than using the manual winder