Toothpaste, as has been said, is a good method of cleaning the stem by hand. Even with Baking Soda in, it isn't anymore abrassive as say 800 grit paper. Don't forget, that after ANY abbrasive is used, it needs to be buffed. Whether that is by stropping by hand using a clean cotton strip (an old T-Shirt is great for this) or by a powered buffer wheel the choice is down to you. The industry usually uses Green Tripoli and a cotton buffing wheel to take off the oxidation from Vulcanite, followed by White Diamond. When finished, use a soft cloth such as a household duster to remove any traces of the cutting compound and give it that real shine. Acrylic is a much harder substance and doesn't oxidise the same way (or extent) as Vulcanite. That can be buffed out using White Diamond followed by a soft cloth buff. Amber, is a whole different ball game and extreme care must be taken if using a mechanical buffer. It might take longer, but I always do amber stems by hand and never use mechanical buffers.
Remember, the higher the speed of the buffer, the more likely you are to 'melt' the stem. Always ensure you have sufficient cutting compound on the wheel too.