my question is how do go about the cleaning on the outside of the stem.
Heres what I do: Cover the tenon with a thin layer of petroleum jelly, then mix up a good Oxyclean soak. A little tub full of warm water and one whole scoop of Oxyclean is what I use. Let the stem soak in this mixture for anywhere between 15 minutes to an hour, depending on how funky the stem is. Once the soak has done it's job, take it out, rinse it off, then grab a Magic Eraser cleaning pad, and go to work on the brown crud on the outside of the stem. With a little elbow grease, you should be able to get a good portion of the brown stuff off. After that, I rinse the stem again, then hit it with the lowest grit of MicroMesh Sandpaper to get any residual oxidation off. Once you have the oxidation gone, scrub at the stem with the 8,000 grit sandpaper, then the 12,000 grit sandpaper, and that bad boy will look like black glass. As a good preventative measure, I also give my stems a good rub down with some Obsidian pipe stem oil for good measure.