Absolutely the right call. Didn’t want to be all doom and gloom, but a dedicated wheel refurbisher will remove the tyre. Sounds basic, but given any corrosion on the alloy face could be on the rim too, then it all kind of makes sense.
In addition, whether 1k or 2k paint, it’s impractical to paint an entire rim with aerosols. There are a few tools out there regards aerosols and trigger sprays, but between masking, weather (wind or flies and other debris), it takes what should be straight forward on paper and turns it into a nightmare.
You’ve already said you’re a perfectionist. On the positive, if they are genuine Audi alloys, then that’s half the battle.