Immediately ahead: I'm not an expert in such a thing!
I got a defective laptop cheaply in my area online, got it up and running.
Only Wi-Fi does not work, since the two antenna cables are cut (Whatever the reason, it was not me…)
My question now: can I solder them together cleanly or should I get new ones?
You should get new ones, if you just solder them together, they have the wrong impedance, so the Wi-Fi may Will not work or will not work properly.