I'm not sure if this will work without a battery. Not all hardware can run straight from an external power supply.
I'd say your best bet is to leave the battery in, use a player that doesn't stop in the bootloader if it detects power (some players do charging in the bootloader, which is annoying in this case), and set the car adapter mode setting. That has the effect of pausing playback when external power is removed. After the idle timeout expires (again, you can configure this if the defaults don't suit you) it will then switch off.
Of course you could connect the power supply to the battery leads, but I'm not at all sure if that's a safe or sane thing to do