You can "tune in" CW at any pitch you wish (until the receiver's IF filter rolls everything off). I'd never listen to code at 2kHz, that's annoyingly high.
Most of us listen at about 600-700 Hz, maybe 1kHz on the high side and 300 Hz on the low. But if you use a receiver, you can just tune in to almost any old pitch that sounds good to you.
Unless you have total hearing loss, I doubt "hearing" the code will be much of an issue. Use headphones and adjust both pitch and volume to whatever works.