I used to scrub DD1's toddler shoes under the kitchen tap after one of her regular steppings in dog poo on the pavement, and then I dried them on the kitchen radiator. My mother disapproved, not because of any hygiene issue (of which there don't appear to have been any) but because she said I'd ruin them drying leather shoes like that. They only had to last three or four months so I didn't agree with her assessment.
I was proved right in not worrying about shoe wreckage because a couple of years later, my health visitor asked me if I had any toddler shoes that might do for another child. I had cleaned an polished all my kids' baby and toddler shoes, put them back in their original boxes and stored them in the loft. I don't really know why, but it turned iut good because I gave them to the HV and she took them to the baby clinic and was able to give them to people who were struggling. Seems the fact they were all shiny and in their boxes made a big impression.
So, yeah, jings, if you've got this far, scrub them under the tap, dry them and carry on using them.
PS why would you tell your DH you'd bought slippers? Ever?