You best bet would be to rip your CDs and use a small media player, even an ipod or an integrated or receiver that can play files from USB. Most blu ray players can do this, but in today's world most blu ray players have dropped analog connections and you need to use hdmi connections to a receiver or integrated wtih HDMI (which are becoming more common. The Sony x1000ES and 1100 models can play from USB and you can use an iphone app to navigate the drive and they have retained two channel analog connections.
Supercharged Song Towers, Oppo BDP-203, Anthem MRX-520, LG B6 OLED
Headphone Rig: Oppo BDP-95, Burson Audio Soloist MKII Headphone amp/ Sennheiser HD800S, Sennheiser HD650