I don't think anyone here can give you an accurate answer to your question unless you know what exactly caused the death of your other animal. Did you get a necropsy done? Because the amount of factors that could have gone into what happened to your animal is almost limitless. Without knowing specifics, I certainly can't give you a valid answer.

I would do what people normally do; clean everything with a diluted bleach solution (10% or so should work). Throw out anything porous, and get a can of prevent-a-mite, I absolutely would not assume that the mites will die in 10 days without a host. The adults might, but the eggs they laid will hatch in 30 days if you didn't already kill them yet.