So, despite what the question implies, I went ahead and waxed my old cassette with the chains, with mixed results.
I gave the cassette a soak in mineral spirits, followed by denatured spirits and then soap water and a rinse in plain water to clean it, the same as I did with the chains. I made sure to write down where the plastic spacers were, but I have since misplaced the piece of paper.
As for the actual waxing, I put the individual sprockets in the wax for about the 45 seconds the guide I was using recommended for chains, then fished them out and left them to cool.
The first problem was that the thin layer of wax on either side of the sprocket added up enough that I ended up having to rub some of the sprockets together to thin the wax layer enough to even put the cassette back on the bike. I had trouble indexing my gears afterwards, probably because the wax still threw the sprockets' positioning off. I suspect that this is also why my cassette came off mid-ride some time later.
All in all, I might check to see if any of the wax remains on the cassette, and if it does try waxing a new cassette still on the packaging tube to see if that mitigates the problem with the wax getting between the sprockets.