Edit: Perhaps a portable amp/DAC would be the answer for using with a portable CD player?
Consider the Objective O2+ODAC combo. There might be important differences between buying O2 and ODAC as separate pieces and as a single unit. I remember that they had to remove the batteries to make room for the DAC, so I don't know if how portable the combo is. But I'm not sure, so if you think you might want it, call / e-mail JDS Labs about that. (They're also willing to customize the gain depending on how quiet/loud you listen and which headphones you'll be using.)