I have a prewar Contax II. They may have modified the new postwar cameras for better 135 cassette compatibility.
Anyway normal film still works in mine so a standard spindle should work on the receiving side. My camera came with one, which I believe was slightly different: from a normal (empty) roll of film you would have to flex off the shorter of the protrusions at one end of the spindle. When using old Contax cassettes (for rolling your own and a better fit inside the camera) the shorter spindles are a must or the whole system will seize up.
And the receiving spindle should have a slit to enter the film. Some film makers tape the end of the film to a solid spindle, others have that slit.