Well, I took some baking soda and water, made a paste, and rubbed it on the tail of the razor with my finger, to see if it would have any effects on the metal. I looked at the tail with a loupe before and after, and found very little difference. The loupe did reveal some minor surface scratches on the "before" look, which I hoped the baking soda might help buff-out. Turns out it had no noticeable effect. I suspect the baking soda particles are just not hard enough to do anything useful. I guess after hundreds of laps on a soda-pasted strop it might have some sort of effect, but at that point, how do you know if it's the powder, or just the regular strop that's making the difference...

I'll keep the baking soda for the kitchen and for teeth brushing, and I'll order some CrOx or other suitable compound for the strop.