I really like Marv's suggestion for your application.
Adding a little to it though. since you will be re bending the wire in the opposite direction after machining to a fix it on the model use as large of a cylinder mandrel as you can make the wraps as he stated tight and close together even soft copper would be machinable but you must hone your cutting tool till it is as sharp as you have ever made one just as if you were cutting neoprene to make hydraulic piston seals take very fine cuts at medium high to high RPM. And try not to allow it to heat up as you are machining it as it will expand and become loose on the mandrel
For copper you could even do this on a wood lathe or drill press and use a file like you would dressing any final cut