Imagine soft, washable, water-tight, polyester-lined pouches that you stick into your child's pockets with double-sided tape. You squirt in some non-toxic disinfectant gel.
Thereafter, whenever your child inserts their hands into their pockets they get cleaned. On the inside of the pocket, there should be something that is interesting to the touch. It would keep your child exploring/fidgeting with and disinfecting their hands in the process.
You insert the pouches into your child's pockets only when going to public places or somewhere where there is a high chance of them picking up a harmful germ.
This idea could be crowd-funded via Kickstarter or similar.