Animals who SI?!

Do you mean an E-collar when you say "lamp shade hats"? The vets use those so your pet won't tear up a wound or any stitches they had to get.
It's in their nature to try to lick it because, like they lick their coats they try to clean it or relieve any strange discomfort they're feeling.

When we get stitches, we understand what they're there for. Animals don't, but they're not trying to hurt themselves. They just become confused.
My dog has had to wear an E-collar after trying to mess with a wound but after bringing her home and giving her lots of attention and love she was calm and recovered quickly.