Keep in mind that the volume controls on budget CD players are generally digital. That means that when volume is lowered from max, it affects the bits and thus the resolution of the output signal. You might be better off picking up a used Creek OBH 10 or 12, a passive remote preamp often available for as little as $150.
Do a search here on Audiogon on analog vs. digital CD volume control for more information on this.
Do a search here on Audiogon on analog vs. digital CD volume control for more information on this.