I'll agree with both ABerrant and PaintPowder1, with just one proviso. There should be a little diagram on your 800mA adapter showing whether the centre pin of the connector is positive or negative. There should be a similar diagram on your CD player. Please ensure that they're both the same.
Most modern electrical devices are fitted with a diode, in the power input circuit, which prevents damage if a 'wrong polarity' power supply is used. (If so, and you've got the wrong polarity on your adapter, the CD player won't work but no harm will be done). But there are still some manufacturers who omit such a diode; using the wrong polarity with such a device would be disastrous.
Chris