I've found that the easiest and most effective cleaning method is to put the knobs in a solution of biological washing detergent and warm water, and leave to soak for a few hours.
After this treatment most of the muck can just be rinsed off, and a little effort with an old toothbrush will usually shift anything that remains.
This works because much of the dirt will be organic in origin (mainly oils and debris left by fingers). The biological additives in the detergent digest these, leaving the plastics unharmed.
I've used this method many times. So far I've not had any problems, even with knobs with bright metal inserts.
I've just done the knobs for my Bush VHF81. This set is looking really good now, and I'll be putting some pictures in a blog soon.
Keep listening!