I don't really understand your question.With a single rotor with the coils self supporting or on something non conducting such as wood there is no eddy current problem.
As you don't say what your backing is I can't help much, but if it is wood, plastic , resin or similar there is no issue and you don't need to take any precautions. If the backing is conducting then unless it rotates with the magnet rotor you will get eddy loss and it could be serious.
The idea of an iron circuit at the back of the stator is to complete the flux path and direct the most flux lines through your coils. If this iron circuit is stationary it needs to be made of good grade magnetic steel and it needs to be laminated in the right direction to break the eddy current path. For your case I advise you not to go this route as a suitable core material will cost more than it is worth and trying to use cheap materials such as crate banding will give very poor results.
The single rotor is a cheap and cheerful design that makes poor use of your magnets but it doesn't suffer eddy loss and will make a good low wind machine. Just expect only about 1/4 the power of a dual rotor.
Using a dual rotor completes the flux path but as the whole thing is rotating together there is no eddy current issue. It doesn't matter a great deal if you don't put any magnets on the second disc as long as it rotates. If you leave the magnets out then expect about half that of a dual rotor rather than 1/4 without the second disc as far as power goes.
Hope this helps, if not try to explain better what your backing is.
Flux