Pressure wash that puppy and hang it on the clothesline.
Picky are ya? ok just dunk it in the bath tub but no bath oils. Shampoo maybe.. Maybe a little conditioner. Blow dry..
or
Protect the cart and stylus VERY well and:
Get Q-tips, micro fiber cloth a little distilled water and time. Don’t reuse the micro fiber unless you wash it with a little ivory and rinse it 1000 times and dry it in the dryer. I keep a cool 50 on hand all the time. 50 in the wash 50 on hand. I use them like toilet paper, on my gear. Once, and in the dirty micro fiber bin (it’s different) it goes, for a soft wash and a rinse, rinse, rinse and dry.. :-)
A little distilled water on a part of the cloth can help remove more stubborn stuff.
If hair is abound, use a vacuum with a controlled suction (a second hole in the line to bleed just in case).
I wax everything I can too. Once a year or so.. Just wax and wipe with MF and toss them in the micro fiber bin..