A 23 khz sound wave will have a wavelength of about 0.6", if your tweeter dome is larger than this it'll have a job reproducing this freq, if its a soft dome then it has a chance of reproducing it as the cone will 'break up' into its resonance modes where only part of the dome (or whatever projects the sound wave) produces the sound wave, however at a reduced level and the device will be more directional (which might benefit you).
I reffered to cheap motorola tweeters further up (motorola ksn1005, affectionately known as 'lemon juicers' from their appearance and sound quality), I suggest you at least look into these, they have a response well into the ultrasonic range, and because they are horn loaded you'll probably get better dispersion, and being piezo are generally high impedance which means they are easier to drive and I've found them to be quite hardy, looking at pics of 'cat scarers', they look like a similar horn.