I think the best way of dealing with this would be to publicly embarrass the man, by taking up a collection to get him psychiatric treatment for his “severe, crippling fear of dogs”.
Lay the sarcasm on thick, complementing his police department for hiring “the handicapped, *despite* his morbid obesity and psychological problems”.
Then perhaps question their judgment in arming a person who lacks the “emotional stability to work with the public”, and ask if they have hired any other officers who may present a “public risk or menace”, because of their deep seated fears and phobias.
“We certainly hope that none of the other officers are so terrified of say, small children, that they feel they must shoot them after experiencing a neurotic panic attack.”
Maybe he was just jealous of the dogs energy and ability to move.
I like your approach, unfortunately sham has been outlawed for decades now ;(