Samuellaudio: My best answer is conditional; should the CD be smeared with greasy fingerprints most likely , should the CD have non-organic smears most likely from breath vapors to very mild cleaners will do.
LPs are side walled deep gorged affairs that can trap all sorts of junk, CDs flat and shiney ,no gorges here only surface junk.
Personally, I steam clean LPs and rarely CDs ;I find steam superior to the exclusive use of chemicals & RCM's. I have the RCM's , cleaners and steamers so I use them all very sucessfully to cleanse my record/CD collections.
I am taking this thread to acknowledge experiments with patient pending active micros created specifically to devower organic materals on non-organic surfaces including vinyl. The initial results are mind-blowing in terms of surface cleansing.The listening experience is so different on LPs and marketly improved for CDs. As far as I can tell from years of experimentation , no cleaner on the world-wide market does a better job. The product continues in the experimental phase and is not yet available/ released to the public.