Ok, found the wire.
And what size of shrinks would I need to get it properly reshrinked after the soldering?
I would say 50mm for the long side but what for the narrow sides 100mm?
Apart from that: HC is out of shrinks, that's just great...
But I just got a better idea since I don't want to wait another 2-3 weeks.
I will see if it works out the way I planned.
I would still apreciate every help on what solder to use and on how to do this.