I usually create a blank layer and set it to darken. I sample a color near the shine, and paint over the shine, resampling as needed. Then I lower the layer opacity to about 10-25%, and repeat on areas with more shine as needed. I found if I go over 25% it gets too plastic-y. I like painting better than cloning because I don't need to be worry about running into a sampled area that I shouldn't be using, and I like doing it on it's own layer so I can go back and adjust it later if it needs it.
What a great tip! I had been using clone/healing brush in the past to fix any hot spots. Painting on a new layer works so much better. I HATE sampling, resampling, etc etc with the clone stamp.