The bar of soap applied in advance works pretty well with wood smoke residue. However, since soap (even the so-called biodegradable kind) is toxic to aquatic life, using the soap bar means you can't use your pot for dipping water, something which I do frequently.

I keep my pot in a silnylon stuff sack. That's partly so if I have to use it on a fire, the soot stays inside the stuff sack and doesn't get all over my pack. The stuff sack also keeps the lid on the pot, useful when packing items inside the pot.