The preferred method is to blot as much as you can with a towel first. Then wash with a liquid soap that breaks down grease, like Dawn dishwashing liquid. You have to break down the delivery substance. I have been exposed to OC spray, for training. Kind of sucks.
Agreed, your method sounds better for external contact with pepper spray.
If you happen to get it in your mouth though, milk (or sour cream, butter, or any food oils) would probably be less likely than dish-washing detergent to make you gag. As I said before, my experience with capsicum comes from eating HOT hot sauces.
BTW — capsicum gives you the “sensation” of a chemical burn. Unlike (say) mustard, garlic, and other “hot” foods — which can easily give you an actual chemical burn.