Don't believe the story that you should not get chips wet. That is true of the old 'true clay' chips, but modern chips are made to take almost anything including alcoholic drinks spilled on them. I have soaked a chip for a day or more with no damage. Too much scrubbing with soap and water will remove some of the plasticizers; just don't overdo it. I find that Meguiar's Mirror Glaze works well to rejuvinate dried out chips. You can get it in sports car shops (used on plastic windows of cars and airplanes).

No need to buy special clearers; any soap will work fine. If you still have a prejudice against soap and water, naphtha on a cloth will remove most grime very quickly. Use only enough to moisten the cloth. This will also remove the 'green crud' that seems to grow on some of the older chips with shiny surfaces. HCE mold chips seem to be particularly susceptible to this stuff. A quick wipe will do it.

Don't use fingernail polish (acetone) for anything other than cancellation removal. It WILL dissolve modern chips. It works on stamp-cancels only because the center inlay of most modern chips has a plastic coating. If you get the liquid on the rim of the chip, it softens and will stain the rest of the chip.

I agree with Mera's comments on hot stamped chips. Don't brush the hot stamp. But with a little practice, you can shield the center with your thumb and clean the rest of the chip with a brush.

I tend to clean two types of chips: those that have so much grunge that I'm afraid to handle them, and those that are almost new and have just a little surface dirt, easily removed. Those in between I prefer to leave alone.