What you want is construction history. You want to extrude a circle along a path that describes that shape. And with construction history, any size change in the original circle will be reflected in the resulting extruded mesh. Since it's a tubular shape, it's pretty straight forward to generate a path curve to extrude a circle. How are your scripting skills?
The idea is to get the center of all the edge loops. Create a variable to store the centers.
Start by selecting an edge loop at one of the boundary edges of the tubular mesh.
Convert edges to verts and get the center.
Convert the verts to faces and back to verts...then remove the previous verts. This gets you the next ring of verts to get the center.
Continue this process of getting centers until you run out of verts.
Now create a linear curve by placing a cv at each center location.
Now rebuild the linear curve as a cubic with the same number of spans...this is the path curve.
Next is create a circle and extrude it along the path curve...set the options to "Tube" and "Result position" should be "At path". I can't remember the pivot or orientation settings at the moment. But play with the options of the extrude node until you get what you want. Then scaling the original circle will allow you to adjust the thickness of the tube.
This of course will give you uniform result along the tube. Since you wanted to only have one circle control this, I'm assuming uniform is what you are after. Let me know if any of that was unclear.
Forgot to add those steps only focused on the deformation/control aspect. If you have uvs and textures on the original tube mesh, you'll have to make sure to match the uvs of the extruded mesh to the original. Otherwise, your textures won't work.
