I'm new to wire wheels (mine are stainless). I wear disposable rubber gloves (attractive) and take the wheels off to clean them.
It's a very long job.
I've waxed mine with 'Rim Wax' (Amazon) amd I'm told it helps keep them cleaner.
I'm experimenting with stuff like 'Muck Off) a bicycle wheel cleaner I think, but it's really only elbow grease and time that's getting them clean.
