How to clean Karat 17D3 stylus?

They make special stylus brushes you use wiping back to front. These are usually used dry. I do not care for them myself. I use inexpensive artist brushes. I clip the bristles about 1/2 way to stiffen them up a bit. You can dampen the brush with distilled water and it is soft enough so that you can wipe the stylus gently in any direction. Do not use any other solvents. many of the styluses are now glued onto the end of the cantilever and more aggressive solvents than water can damage the glue.

Have you examined the stylus and cantilever under a microscope?  That will tell you how dirty it is now.  Then you can have another look after whatever cleaning procedure you decide upon.  Yes, the cantilever is very short (17mm), but I am not aware that cleaning the stylus is especially fraught, compared to cleaning styli on longer cantilevers.  I'd use Stylast #4 followed by the Stylast stylus brush, carefully. ((I've got a 17D3 too, and for casual cleaning between sides I have used Magic Eraser.)

Thanks, guys. I’ve always used a brush followed by a liquid cleaner but I’ve read that you have to be careful with any liquid as if it gets on the rubber support it can harden and damage over time. I never realized just how tiny the stylus were on these things. A microscope would be nice but I don’t have one.

I blow on it

@czarivey 

I blow on it

I highly recommend you do not do that. Peter Lederman of Soundsmith has said blowing on your stylus/cantilever can result in small particles of saliva build-up that attracts dust and can become hardened 'gunk'. They see this all the time when cartridges are sent for repair.

If you need to 'blow' on the stylus, get a handheld blow/bulb that photographers use, as example.