What we really need is a pot of super-hot moulten solder, into which we can simply dip the ends of the wires to both strip the coating as well as pre-tin the wires at the same time. What we really need is a solder pot.
We used to have a solder pot, which did make soldering a little easier. Except it was really smoky. Not a little bit, but really, really smoky. The reason for this is the flux core of most lead-free solder on the market. After melting a tube of Maplin's finest in the pot, there's a sticky, tarry, residue left in the pot. And when this gets hot, it really smokes!
What didn't help was that the pot we borrowed off Matt (ours had gone missing during one of numerous moves over the years) looked like it had been used as an ashtray! Even after loads of scrubbing, and even with brand new, fresh solder, it still smoked like crazy.
We skimmed as much crud off the top of the solder as possible, while it was still moulten. We then placed some kitchen foil inside an eggcup and poured the solder into it. Then left everything to cool down.
Cleaning the solder pot was no easy task! Using a screwdriver head, craft knife and pan scourers, we managed to get a lot of the black off the inside of the pot. It wasn't perfect, but we managed to get a lot of junk out.
The actual solder, meanwhile, looked bright and shiny, with no trace of the impurities that made it so scummy-looking when it was in the solder pot earlier. With both solder and pot cleaned of any flux residue, we put the solder in the pot and let it melt.
This time, the solder melted without even the teeniest whiff of smoke! So little, in fact, that it made our heath-robinson smoke extractor (a PC fan and a piece of aquarium carbon filter) unnecessary. Now we had a nice, clean, smoke-free way of preparing our magnet wires, prior to soldering.
If you have any trouble with a smoking solder pot, try cleaning the solder, as well as the pot, and see if it improves things!