I've had good results with all kinds of small items, especially 3-D complicated parts, using a sonic jewelry cleaner. In addition to jewelry, they are used to clean eyeglass frames, where the hinges are small, intricate and fragile, both metal and plastic. They get gummed up from skin and hair oils, hair care products and dust from the environment.
Some use plain tap water, others soap and chemical solutions. Maybe your wife has one already?
You could try venting steam from a vaporizer into the piece, also mix a small amount of dish soap (cuts grease/oil well) or alcohol - like Listerine into the water first. Essentially a mini steam cleaner. Shaking vigorously with warm / soapy water first seems like a real quick and easy thing to try first though.