Most soap also leaves residue. It’s bad enough trying to get rid of it around the sink and on transparent shower doors, so just imagine getting it on CDs. To give an idea of how harsh some soaps are, I once ruined a pair of spectacles trying to clean with soap after getting a smudge while out visiting, as it not only removed most of the coatings, but also made the lenses hazy (looked as if they were cleaned with fine sandpaper), which I obviously had to replace. It was a costly mistake.
Generally a plain soft tissue is fine by wiping from the centre out to the edge to remove dust and fingerprints. If you use cleaning wipes, make sure they mention they are suitable for CDs. I have used washing up liquid and water in the past to clean discs without any issue, but I wouldn’t do this on irreplaceable discs just in case, such as a CD of backed up photos where the originals have been lost.
Avoid using medicated or scented tissues, as these will more likely smudge the surface, much like how these tissues are not suitable for cleaning spectacles.