I had a local amp tech tell me that you have to have the iron really hot so quick in and quick out so the insulation has no time to melt.
Try pre 'tinning' (just the least amount of solder you can) the striped end of the wire
and the eyelet/turret/switch contact/etc. 1st.
This helps the solder connection get 'wet' quickly and suck up the solder. Also it helps to use a little solder flux paste, brush a
little on both parts to be soldered, just a little, then 'tin' the parts. It helps clean the parts of any oxidation when heated, so it sucks up the solder.
I know you asked about transformer fly leads but, for other connections you can use Teflon isolated hook up wire, works great. Doug sells it in different colors.
Or, cloth
push back hook up wire, (there's other 'cloth' covered wire out there that is PVC insulated wire that has a cloth braid over the PVC for looks. Some guys here use it and like. I would think that the cloth braid would help hold the PVC in place when heating it up?) Doug sells the 'push back' in different colors, another very good option.
My question is for leads coming off of the transformer wires, the wires almost always tend to strip off when trying to solder. So i go the length of getting some heat shrink on the end of the wire so that the insulation doesn't come off and that way I can get the leads tight up against whatever I am soldering to.
I've tried that and it works pretty good.
One thing I've noticed is that if the PVC wire I'm soldering is bent (in a rounded hook shape) at the very end instead of being perfectly straight, the PVC comes off real quick! (Even with pre-tinning.) As it heats up the PVC moves/pulls away from the wire itself, the PVC is trying to straighten itself out.
It takes practice (I'm still getting better), you'll get it, hang in there.
"You have to break some eggs to make an omelet." Brad