Hi and welcome to the forum,

In answer to your question, yes there are plenty of good CD players out there for around $120.00 which will do the job very nicely. Most, if not all of them, will have dedicated left and right line level audio outputs with female RCA jacks which you can easily connect to your headphone amp. Most will not have their own (built-in) headphone amp or even a headphone jack.

Sony, Denon, JVC, and NAD are just a few of the brands that you might look at.

Double your budget and buy used from AudiogoN. Don't panic when you view the CDP listing, just ignore all the $1000, $2000, $3000, +++ prices.