The reaction channel is just (the indicated) one.
The point is that the experimental cross sections are (naturally) given on 63Cu and 65Cu, respectively, and not natural copper (despite the fact that natural copper was actually used). This means that you should more conveniently run two separate simulations, with pure isotopic composition of 63Cu and 65Cu, respectively.
This way, you should rather find about 65 mb (63Zn) and 160 mb (65Zn) at 4.32 MeV and 110 mb (63Zn) and 230 mb (65Zn) at 4.63 MeV. The discrepancy with the reported measurements can be easily understood looking at the huge gradient displayed by the excitation functions in Figs. 2 and 3 up to about 6 MeV.