Making connection to very fine wire?

I'm the one who misunderstood. For some reason, although you did not even imply it, I took it to mean that the copper would dissolve over time.

I didn't make it very clear; there might be a long-term effect too, but I haven't heard about that.

If you use copper-loaded 'Savbit' it will prevent any copper dissolving and will also make the soldering iron bit last longer (which was its original selling point). Silver also dissolves in solder, which is why silver-loaded solder has to be used on the silver-plated ceramic tagstrips of older Tektronix oscilloscopes.

Any links to this wire grade?

I've seen solderable, but would be really surprised to see self-fluxing.

Any soldering will produce brittleness, in fine gauge wires, so crimping preferred - both with strain relief.

RL