How to cut WAV or Nero digital off at exactly 20000Hz?

I'm getting a sony walkman nwz-s618 mp3 player. The response rate is 20-20000Hz.
Does this means it filters frequency outside of that range (even if I use headphones
that goes outside that range, like up to 23000Hz)?

If so then I want to encode wav or 320kb/s Nero digital files such that the frequency is cut off at exactly 20000Hz.
This is because I do not want any wasted bits in a higher frequency that is going to get filtered
out. I would rather those wasted bits get used to improve the part of the file that is within that
range. This should make the encoded spectrum wave (shown in adobe audition) resemble, within the range, as closely to the source spectrum wave as possible.

Now when I encode with lame cbr at 320kb/s the file is cut off at about 20000Hz. While this is somewhat fine, I would rather use a more accurate codec such as wav or 320kb/s ACC Nero digital instead. But with these I have no options on how to set the frequency to a max of 20000Hz.

Are there any programs or encoders that allow me the option to encode wav and or 320kb/s Nero digital to be cut off at exactly 20000Hz?

Thanks!