Can I use a 4.5V/ .8mA wall wart with this CD player?

Should work fine, if the plug is the same size. The amp rating of the plug just means the power available. Since your appliances uses less, it will, well, use less.
Example is plugging a 100 watt (0.1 amp) light bulb into a 20 amp branch circuit. Works fine, and uses 0.1 amps.
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