I recommend people who have a soldering iron to start experimenting with enameled wire. It's easily sourced from any random coil/inductor/switching transformer/broken speaker even. Dip the tip of the wire in some flux and keep it on the tip of the iron for a bit so enamel clears away and tins the wire.

This way you can solder the thin wires in crammed places, don't have to stress about them shorting out anything they touch, easily routable and they don't put stress on the solder joint, like a regular thicker wire would.

Working with this type of wire made things easier for me in these sorts of situations. And it's perfectly adequate for signal (withing reason, if not very high speed), and even some power, few mA needed for these kinds of chips is no issue.