Hi Marie,

You are correct that you could use path-constraints for the cables, but depending on the animation required, you may not need to use path constraints. For example, if the animation you would like to create is something like the following:

The above animation’s setup is here:

A bone is placed at the bottom of the hanging cable, and the cable is moved so that it is pulled by the bone in the animation. Such a movement does not require any constraints.

If you would like to see another example, the rigging of the bag in mix-and-match-pro may be helpful.

I hope this will help you.

Let me add one thing! The first example used quite a lot of vertices, but depending on how much you want to move the cables, you may not need so many. If the movement in the example animation is enough, roughly half of the vertices would be enough to make it look good.

I'll chime in just to add a couple suggestions.
Anything that is curved is usually a pain to rig, so generally, it is best to either keep it as simplified as possible, or to rig it straight then bend it after rigging, or a lot of vertices will be needed keeping these as base images.
Blog: Mesh creation tips: vertex placement: Curved, bendy surfaces using only 3 lines and weights

If you realize that the cables are only a minor part of the rig, you may wish to simplify the rig even further:
I'd go even more extreme than that and just make a square because that image is curved, and weight the top to the body, and the low end to the bone.

OR using even less resources, no mesh at all, a bone at the top where the cable is attached, and I'd only use shear to move the cable a little.
Tools - Spine User Guide: Shear tool

With curved stuff like that, either you fight it and add lots of vertices, or draw it straight, then curve it, or you give up and keep it as simple as possible!
Mostly considering this from the perspective of "it's just a decoration and I'll probably even forget to animate it most of the time"
(But my way is not necessarily right, it's just me wondering "how far can I push this to simplify it?")

If as mentioned above, a natural movement is required, and the cables are an important part of the rig and their movement is important, then I think that Misaki's solution is perfect!