I suggest that you give details of the iron (and tip) and solder that you are using and a close up photo of the wires that are being problematic.
The iron temperature control may be faulty and the iron just not getting to soldering temperatures. Or you may have it set too low.
The thermal mass of typical USB wires is so low that, if the solder actually melts freely at the tip end when not soldering anything, it should do so when soldering these wires.
Get them working on their mathematic skills, instead. You can give them a really good head start - mine could solve simple differential equations at age 11.
I'd suggest peeling off just one strand of the wire and use that. You will need to insulate the wire from the nail - Wrapping paper around the nail will do. You will need to insulate the wire from itself, so that adjacent turns don't touch. You can just space the turns out along the paper sleeve. That should do the trick. If you have twine, you can wind that on with the copper wire and use the twine to keep the turns from touching each other.
Oh to straighten copper wire, if you don't know this trick - hold your nail in a vice and wrap a single turn of copper wire around it. If you then pull on one end of the wire, keeping a little tension on the other - with a bit of practice it will give you a very straight end result, as the wire pulls away from the nail.
The standard way of looking at this is to consider a capacitor-resistor series combination going to ground. Connect a 10v (wrt ground) supply to the capacitor and the voltage across the resistor rises to +10v, then decays. Now connect that capacitor to ground and that same resistor gets -10v across it, which then decays. Whatever is connected to the capacitor "top" terminal has to be able to sink current as well as source it.
That's what generators in simulators do - they have zero internal impedance (usually). They sink currents as well as source them.
Lots of people use them for something similar. Obviously, the situation changes once the lines are power lines and not signal lines. If you can stabilise the result and add strain relief.
I think that it is the same stuff, just will propellant added in the aerosol. A small squeezy bottle with a needle is better if you have live stuff nearby - but you can always fill one from an aerosol
Assuming that the ribbon cable is standard - you could consider adding TWO IDC connectors, side by side. Then slice the cable through between them. Then add a standard extension cable to link the two. Indeed if one of the two is male, the other female - the extension can be removed if the thing is relocated to where the extension isn't needed - or a longer one is needed.
I confess to having done this sort of mod several times, myself. It's also quite an easy way of sticking a protocol analyser/sniffer between the two and/or modifying the data that is sent on its way. Or adding an additional sensor (even of a different type) and converting its output to something suitable.
Switch cleaner?? I use RS "own brand".
You could use something like this:
The diodes at least provide some steps - which just LEDs and resistors don't. The dissipation in the main series resistors will be quite something, also. (You will probably need several resistors in series, if you use standard ones, with their standard voltage limits).
How I would do it is to use two digital IO pins on the processor to generate the reference square wave. Put the sensor plus a series precision resistor between them and just pull one IO pin high as the other is pulled low and then swap them. That presumes that IO pins can both source and sink IO current. Then take the junction between the two to an Analogue in pin. You get two measurements each cycle. Use a lookup table of values and interpolate between them. If you wanted more precision - add more series resistors of different values covering the range of humidity that you want to sense, going to different IO pins. So you can choose the IO pin pair that brings the centre point between sensor and resistor closest to the mid-voltage point. It's effectively a balanced half bridge arrangement - using the precision of the resistors to determine overall measurement precision. OK it ties up several IO pins - but microcontrollers are so cheap, I'd probably just dedicate one to this sensor and that's all that it would do.
I'm assuming that those "v"s are meters and not constant voltage sources. A 2.4v zener does NOT have exactly 2.4v across it. A 1.2 v supply will not be precisely 1.2v. Both will also vary with time and temperature. So, in practice there WILL be a dc component across the sensor - which will destroy it.
On a KISS basis - I tend to just use a bimetallic switch or omit the temperature control and just run the fan from power up. It's possible for a processor to suffer some non-handled exception where it no longer executes the temperature management routine.