Not strictly on topic, but can I tell you my 'shit' treadinf story.
I was walking into work once and trod in a huge pile of dog shit, so much that I semi 'surfed' the shit, and ended up falling in it. It was on my shoe, in my shoe, up my trousers, inside my trouser legs.
A chap, seeing me on the floor rushed over and picked me up, then smelled the shit and dropped me back in it!
I was an hour from home, by train, so I went into work and cleaned myself up as best I could!
Shit surfing, is what we call this sort of thing in our house.
Realistically, shit, and shit surfing happens. Learn to live with it , with the minumum upset and hassle. Binning the shoes is a huge over reaction. Scrub off what you can and soak the damn things. It isn't rocket science.