Wow..... I had to step back in time on this one.
From the looks of it you "do" have a separate CSD and Generator. I never changed either on an older 737-300 back when I was starting out.
So, yes the generator can be removed by itself an sent to shop. Same way with the CSD (the generator would have to be removed first).
727's, 737-100's/-200's and the DC-10 had separate units. I assumed the 737-300 and newer had IDG's. I was wrong on that assumption.