It may be possible to get the zinc with a sulphuric acid leach. The copper should stay behind, and the iron can be left largely unaffected under the right conditions. Thermodynamics are on your side here.
The next challenge is getting the copper, while leaving the iron behind. This is more tricky. You can try a leach with sulphuric acid and hydrogen peroxide. You will have to control the exposure time so that only the copper goes into solution, while the iron remains. Thermodynamics are against you here, so you need to use kinetic or time barriers.