Hi Tom, I understand your lack of enthusiasm for a total rebuild of a fully functioning machine. There are a couple of things I would recommend stripping down. This engine is air cooled, there is a large fan in the flywheel housing, that blows cooling air around the two cylinders. There is some steel sheet ducting from the top of the flywheel housing around the back of the engine, I would remove this and ensure the cooling vanes on the cylinders are clear of dust, cobwebs, mouse nests and etc. Also clear the small hole at the bottom of the flywheel housing. The crankshaft seal behind the flywheel is made of felt, not neoprene and can leak a small amount of oil, better if it runs out the bottom of the housing than gets blown up through the engine cooling system.
Paint is a difficult question, new paint will not stick to oil or grease so it will need to be degreased and then washed and dried. I have used a low pressure pressure washer for this in the past, just avoid filling the exhaust and air intake with water. This should remove most of the loose paint grease and etc. The red oxide primer is very resilient and is unlikely to wash or flake off, so you should be able to just apply a couple of coats of mid Brunswick green top coat. This can be sprayed or hand painted, remember to mask up areas you don`t want to paint. I hand painted mine, I found that small artists brushes were very good for getting into awkward places.
Bob