I wonder if anyone can help?

My grandfather, who taught me pretty much all the songs I know, died last year, and my grandmother has given me his harmonica (as I've been trying to learn to play for a while) and his Swannee Whistle. I always loved it as a child, because not only could he play it beautifully, but he would let me make Clanger noises with it. (For the uninitiated, The Clangers was a British TV programme, about peaceful little pink creatures that live on a distant planet, and they talk entirely in whistles, all done on this wonderful instrument.)

The harmonica is in good condition, and plays beautifully, (although there's 16 small holes instead of the 10 large ones on my beginner's instrument - tricky!) but the whistle has been put away at the top of a wardrobe for years. It's rather old, I think - it looks to me as though it's made of bakelite, with an ivory bottom stopper (packed with some sort of waxed cord, I think) and brass moving parts. It plays, but the brass is tarnished, and I think it needs a good clean.

Anyone got any advice on doing this, or on actually playing it as an instrument, rather than just Clanger-whistling?

Thank you!