I use a 30 watt soldering Iron (Pen?) If the old wire was well soldered, I cut the wire leaving the solder on the coil. The new wire is trimmed to fit with the insolation cut back on the end. This is cleaned and a little flux added making it easy to tin. The wire is bent in the shape it will be on installation. That way you don’t have to hold it to solder it, and after soldering there will be no strain on the fine wire in the coil. The only heat needed is just enough to melt the two blobs of solder together, and 30 watts is enough for me.
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