P.M.
This is not an easy answer for moms to hear when they've been convinced they need to run a germ-free and dirt-free home, but really, stuffed toys generally don't need to be cleaned. Any germs already on them die within hours of drying out. The fabric covers are not environments that support germs.
And our children's bodies actually need contact with dead germs, live germs, and a bit of everyday dirt for their immune systems to develop properly. Without that input, the immune system doesn't have the information it needs either to recognize microbes that do make it into the body, or to recognize what is 'friend' and what is 'foe.' Medical science has discovered that children raised in the cleanest homes have a much higher incidence of asthma and other illnesses in which the body attacks itself.
One other thing to be concerned about is that the powerful cleaners available today are often themselves chemical hazards. Take it from a person who has become unable to tolerate the load of toxic elements in our modern environment, you don't want to risk overloading your children's ability to detoxify. Protect them by exposing them to as few chemical poisons as possible.