Using a texture only in a node noodle?

After some searches, I still haven’t found an answer to this, so I hope it can get answered through a dedicated thread.

I want to use a BW image as a Mix input for two materials, like an alpha mask. You can’t load a standalone image in nodes, so I have loaded it already as a texture in one of the two materials of the node system.

The problem is that this material and its texture are already assigned to another object in the scene, a rectangular object. So, the texture inherits the size and scale of that object, i.e. it shows up as rectangular in the nodes.

How could I control the size and the other properties of that image? The best option would be to have the image loaded only for the node system, I don’t want to have it assigned to a material that acts only as a placeholder. So the questions are 2:

  1. How can I have an image or a texture loaded independently from other materials, and only used in a node?
  2. If (1) is not possible, how could I disassociate the texture from the material and the object it is assigned to, and control its attributes independently?

Thanks for any help provided!