"fatally shot" is the same amount of words and less confusing

"shot dead" is a phrasel verb, therefore it can (I would argue in this particular context it should) be split:

shot (whom?) dead.

I shot him dead

He shot his wife dead

Cop shot unarmed black man dead (including press-specific omitting of articles because English is stupid)

And yet, we wouldn’t be having this discussion if the wording was actually unambiguous.

I removed one word and added two. That’s not “a lot of filler words”.