Best (and safest) way to clean cigarette smoke residue from dial?

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That's the exact kind of dial this is, my pictures don't do it justice, but the dial is very glossy and smooth.

I might give it a go with an eraser (very gently) if I can't make enough progress with the other suggestions.
As mentioned, start with somewhere on the very outer edge where its covered by the crystal, so if it does any damage it'll be covered when re-assembled and use a soft and small eraser, keen to see how it goes