How to effectively animate a "lasso"?

Hello everyone,
I am currently making an internship in the field of chemical research, and as part of this internship I want to use Blender to make presentations.
I recently started using Blender, I understood some basics but not everything …
For example, I would like to animate a “lasso” but I think to do it very badly because I spend a lot of time to have a very imperfect rendering and I am sure there is way to make much faster and much more effective.

Here is what it gives in frame 1:

Then in frame 94:

Well, here we are very far from a pro render (the axis in gray should be fixed on the torus, the curve is ugly …) but the overall idea of what I would like to do is present.

For now I tinker (it’s really the impression that it gives me) with a bezier curve and hooks. Can you tell me how to get to my goal?

I thank you for your response in advance,
Rota.