@Blue Hills I can't comment on any product other than white spirit. A buddy told me 20+ years ago he did it and it seemed a good idea. I soak a cotton rag and run my finger round the rim a couple of times with the bike vertical. It evaporates in seconds. The cloth is usually filthy and I'd hazard a guess what I'm cleaning off is much more likely to damage brake blocks.
You are quite right about the chain rings and cassette. I only do this when needed which might be every 2-3 months. Starting with a scrupulously clean set up and correct lube the need to clean these is minimal. I keep lube to a minimum, Mickle method, wipe chain with an oily rag after every ride and lube when needed. If it's been a really dirty ride I'll squirt the cassette and chain rings with the garden hose.
I clean my cassette and chain rings as you describe except I have a nicely shaped brush to get deep in to the cassette.
I don't subscribe to the worries people express about damaging chemical getting into the BB etc. Two reasons; I apply any chemical carefully to the area where it's needed and secondly I leave such on the bike for the minimum time and wash off with the garden hose ASAP.
Overall I feel I'm much more likely to pick up damaging stuff from the road surface than careful washing.
I am a bit anal about clean bikes!! 😂