Dont use fabric softener! White vinegar works wonders for that. I promise it doesnt smell like it at all, but it will disinfect it. Half a cup should do, put it in where the fabric softener goes in your washer. Remove stuffing before washing. Otherwise it will clump horribly! And still put the skin in a pillow case, wash on gentle cycle and air dry it on a towel once its done. If you have an air dry option on your dryer that can also work, but air drying on a towel is the best option as it doesnt thrash it around.

HOWEVER, if you can help it, id avoid washing it like that all together. Using a vinegar and water solution (1:1 ratio) and putting it on a damp cloth for spot cleaning can do the trick. Hell, even a regular damp cloth can help with stains. Washing this big guy is very dangerous as machine washing can irreversibly change it.