Any small device can be hidden or damaged. Loose batteries are dangerous to other residents in a CH who may put them in their mouth. A child's music player would have screws to hold the battery cover in place but if it had an opening flap this could be broken off and CDs removed. My grandson has some sort of simple tablet for his music, but that needs charging and presumably the settings can be fiddled with.
When she still lived at home we had to stop buying MIL replacement radios because she always snapped the aerials off (deliberately - what's this sticky-out bit, I don't know what it is so I will remove it). We tried taping the battery covers down on radios, CD players and remotes, but with scissors and persistence she always managed to get the better of us!
We provided a small TV in MIL's room at the CH and asked the staff to tune it to a music radio station if required. They kept control of the remote. Unfortunately she lost interest in choosing her music and TV programmes fairly quickly. However, her daughter found that MIL enjoyed being shown videos on a smart phone, and also enjoyed songs this way, when it was a social event to listen with someone else. Ditto the entertainments in the CH. She wasn't interested in solitary listening or viewing. She needed other people to put the music into context.