Personally I would steer clear of wheel cleaners. I don't even let them near my wheels never mind plastic chrome.
I use a normal wax to shine up the chrome plastic. Remember it's not metal so no kind of abrasive product is really suitable. You are more likely to scratch the surface and give it a permanent hazed look.
What about parafin? Sometimes the grime seems to be "baked on"... normal car wash shampoo doesn't shift it.
Usually (on my badges) I use metal polish but veeeeery gently.
Parafin, i see you old school Ralf S, that's something my dad would say.... no offence there to your age, but there are products that are out there now that will do what your asking without rubbing, like a TFR- traffic film remover apply it leave it to dwell and hose away, or a Cuitus wash, that is also very good, TFR will strip any way but a CW wont.