One of the other residents spied him, asked what he was doing here, and then charged up to my door telling me I couldn’t touch the floors without body corp approval.
This sound like you have a nosey parker bush lawyer for a neighbour. Send the committee a courtesy note telling them what you plan to do and how you will be observing the noise and cleaning requirements in the by-laws, then get it done. It would be different if it was a common area floor outside your unit, for instance. But I really can’t see an issue here.