It is obviously difficult to comment without seeing the mask, but to keep on the safe side there is only a little you can do, unless you have it professionally restored.
A quick blow with a hair dryer on either a cool or a low setting will help to fluff up the fur and remove any long-term and stubborn dust.
The dullness of the coat would be typical for the mask’s age and it has probably faded over the years, something you cannot restore. However, the eyes and nose can be wiped with a damp clean cotton wool bud, though if there is any sign of paint being removed from the nose, stop and use a dry bud.
Open mouth-parts can be cleaned with a soft toothbrush. If you have a steady hand, painted areas can be touched up, though be very careful not to overdo this otherwise the mask will lose its authenticity.