One of the tricky things with equipment of that vintage is how many different materials were used for the various pieces. They really hadn't settled on the relatively small number of somewhat identifiable plastics they use now. This takes some time and easy-going to decide what is compatible with the base materials while dissolving only the things you want cleaned away.
Watch out for reactions with contact surfaces, paint, silk screens, other labeling, etc.
When I've had to do similar work, which of course was with very different equipment, I found that I needed to use several different chemicals in sequence. The most similar part I worked on were concentric wirewound potentiometers on the same shaft as multipole switches. The grease dried up, but they also have complex mechanical stackups.
Eventually after trying other things to get the shafts loose, cleaned, and re-lubricated I did this:
1. WD-40 for dissolving the grease. Spray in, work it for a while, and then spray out. Absorb with paper towels, etc.
2. Alcohol for dissolving out the WD-40.
3. New shaft lubricant. I happened to use sewing machine oil.
4. Contact cleaner that is safe for plastics to clear away anything that flowed in from the alcohol.