Depending on the degree of end finish desired, I would wonder whether this would be better done by polishing a sphere by itself and then attaching it to a rod.

In any case, mechanical polishing would likely cause distortions because it would be done in non-symmetric conditions. This may be possible with an electrochemical process as one alternative.

I did try many different techniques, including CMP, buffing, electro-chemical. It all depends on the materials you use; metals, plastics are all behave different. In my experience, I found that mechanical buffing with right abrasive pastes gives the best results where on copper and stainless steel I could get down to 10-15nm, PTFE was somewhat rougher due to its high compliance. In general you an achieve better surface finish with harder materials by mechanical polishing.  I periodically used optical profilometer to check the local radius of curvature and the resultant  surface roughness.

You can get more details in some of my papers about the procedure.

https://www.researchgate.net/profile/Andrey_Ovcharenko/publication/238370230_In_Situ_and_Real_Time_Optical_Investigation_of_Junction_Growth_in_Spherical_Elastic-Plastic_Contact/links/02e7e52f17a00c0ad5000000.pdf?ev=pub_int_doc_dl&origin=publication_list&inViewer=true

If you specify you project better, people can provide more specific answers.

Article In Situ and Real Time Optical Investigation of Junction Grow...