I wipe the chain off with a paper towel, put it in a mini-crockpot with melted paraffin and allow its temperature to equalibriate, then swirl it around with an old screwdriver, pull it out and hang it up to drain and cool, and put it on the bike. The only slow part is melting the wax. I do two or three chains at once, and at least two for the same bike.
On the rare occasions when a paper towel would not be adequate (eg: converting a used, conventionally-lubed chain), old white gas (camp fuel, petro) or mineral spirits should take only minutes. The biggest problem is disposing of the waste, so much so I prefer just to buy a new chain under such circumstances.
The lifetime of my chains has dramatically improved, and my hands are clean after doing bike maintenance, so much so that when I forget about it and touch a friend's drive-train, I'm a bit shocked and repulsed by how filthy it gets. (One guy I gave a bike to with a freshly waxed chain decided to dump what appeared to be dirty motor oil on it.)
The main motivation for cleaning off the grime before waxing is to keep my wax clean.
Last edited by Cyclist0108; 12-03-20 at 01:45 PM.