You will be able to just reform it. I have wound springs over mandrels from straight spring steel wire in the past too.
In this case you would look at unbending say the 12 ID x 0.8 over a larger rod (maybe 16-18mm to allow it to spring back) of some sort to unbend it to your 16mm OD. Chances are you will also want to control the power of the spring by adjusting the number of coils in your length too so grab some and play
