This artwork you show is now already line copy. After it is separated it is plate-ready. As it is already screened, there should be no moiré problems out of the ordinary rosettes formed by screens overlap. There is nothing more for you to do. Send the a/w to the printer.
Coincidently, Your illustration shows the correct screen angles for CMYK printing. This image is already (coarsely) screened (or magnified).
Conventional (AM) screen angles for reference are:
C=105°, M=75°, Y=90°, K=45°
Screening is used to convert continuous tone into line art. Avoid re-screening the a/w when it is already line art. Re-screening will result in moiré pattern(s) most of the time. Moiré is most evident in darker coverage areas such as cyan.
Stochastic (FM) screening will not affect the image insofar as printing this is concerned.
You can start working on the billing. : )