Which part is the problem - the handles or the gold-plated metal part?
The handles (Cloisonné) are pretty sturdy stuff ... just use a mild liquid dishwashing detergent, a soft sponge, and warm water.
If the gold is discoloured ... that's a bit more of a problem .. since pure gold doesn't discolour. You might try using a red-rubber eraser (like you find on the back end of a regular #2 pencil here in the US) - just rub it over the surface of the metal ... that's how we clean and shine up gold contacts on computer boards. Don't laugh - it's non abrasive, no chemicals, and does work.
But - if all else fails ... take it to a jewelry store and talk to them. It could be that they can clean it with an ultrasonic cleaner.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain