Cleaning the outside of a Meer?

I inherited a meer from my grandfather that was well used and somewhat abused. He had let a cake build up like it was a briar. I took some time yesterday scraping the cake out and cleaning the stem. My problem now is, he evidently handled it with dirty hands and the outside has dark, blackish areas. Is there a safe way to clean off the dirty areas without hurting the pipe? I've found a lot of info on cleaning and restoring the inside but nothing really on dealing with the outside. Any advice is appreciated.