I have a pair of shoes that I want to clean, (not just wipe down but put in the washing machine). I know this shouldn't be done for clothes but how about shoes?
Probably not based on the halacha that allows applying polish if the shoe color has faded but does not permit shining. This may be helpful http://halachahbyemail.blogspot.com/2012/07/polishing-shoes-during-nine-days.html
If it is not a cloth-like material, it wouldn't be considered "kibus". If you can wash your dishes, you can wash your shoes.