Antenna cable is broken. Do I have to replace it?

Well, replacing them will guarantee a fix and guarantee that no further problems arise.

Fixing the wires yourself will cause any variety of problems if you don't do it exactly right. And thus end up costing you a lot more money to replace the hardware they have damaged.

Personally, I'd replace them.

If you fix the wires incorrectly it will cause problems and I just wouldn't feel comfortable with my abilities to not screw some minor thing up.

However, if you feel absolutely confident with your soldering and repair abilities you can certainly fix them yourself.

But I wouldn't recommend attempting it unless you have a lot of direct experience repairing and working on computers, have screwed up a couple so you know what not to do, and know precisely what you're doing.