It is possible that the prohibition against microphones and amplifiers applies. The singer would be amplifying his/her voice which would be a prohibition against Shabbat.
Rabbi Moshe Feinstein, in Tradition Magazine Spring 1974 has a very famous and seemingly definitive article/responsa on the use of microphones on Shabbat.
Unfortunately the article itself can only be viewed with a subscription to Tradition magazine so I can not provide a link, however, below are some of the excepts and summaries that I found from his responsa.
Rav Feinstein distinguished between objects which are in continuous activity, like a water mill, and those which only operate at intervals, like the chiming of a clock. In the former, there is no reason to suspect that the owner has violated Shabbat, since the sound of the mill can be heard continuously from before Shabbat. In the latter, however, there is reason to suspect that the owner set it on Shabbat, since it does not sound continuously. In line with this logic, Rav Sahul Yisraeli reasons that since we follow the Rema’s opinion that we are concerned about creating suspicion, and microphones fall into the latter category (where there are grounds for suspicion since it is not in continuous use), we should forbid the use of microphones.
In the first responsum (Igrot Moshe OC 3:55), Rav Feinstein wrote: “One’s speech causes [the circuit] to contain more electricity, and it is possible that this is a melacha, for the nature of electricity has not been clarified.” In the second (OC 4:84), he elaborated: “The electric current increases according to the volume of the voice ... We can see this when we attach to the microphone another device measuring the current ... We [also] know that the microphone uses more electricity when someone is talking [into it] than it does when not in use. One who employs electricity on Shabbat may violate a biblical prohibition, even where there is no hav’ara; practically speaking, this matter requires thorough investigation.”
He added there, “The voice heard via the microphone is no longer the voice of the speaker, but rather an [electrical] impression of his voice ... This is a possible biblical prohibition - that his voice makes an impression on some component of the microphone. Despite the fact that this is not considered writing, for there are no letters, nevertheless there is reason to suspect a melacha [is involved], since something new has been created by means of which an amplified voice can be heard. Perhaps this violates makkeh b’patish or boneh; [the question of] the actual melacha involved must be analyzed.”
Therefore, if CD players are amplifiers, just like microphones it would be prohibited to play even if the person playing and listening to the cd play is a non-Jew.