I wouldn't consider using Brasso on anything other than the few specific metals it's intended for. The main "polishing" that Brasso does on brass is chemical - by reacting with and "flushing off" the oxidized surface of the metal. The "vehicle" is a mineral oil that will likely penetrate into any exposed wood, and be very difficult to remove, if you decide something else needs to be done.

As Bigchuck suggests, a violin or guitar polish should be easy enough to find at your local suppliers, and should certainly be the first thing to try. If you feel you must have something more abrasive to get some scratches out, you should be able to find dry powdered talc, whiting, or pumice that you can use to make a fine paste with a little water or with an appropriate vegetable oil to rub with a clean soft cloth.

Most "kitchen cleansers" are too abrasive, but the last I heard the "Bon Ami" cleanser still contained only pumice, with a mild water soluble detergent, so it might be suitable for cautious use.

The sort of "haze" described is usually the result of moisture (and other "body" things) penetrating the finish, and is unlikely to be helped much by anthing short of removing the finish and putting on new finish. Doing nothing is often the best choice.

John