My reaction would be to roll my eyes. It’s a mouse, it’s outside, they’re not associated with dirty conditions like rats are, just leave the poor thing alone.
If it’s inside the building by all means get a trap but when it’s outside in its actual environment you’re just randomly killing animals in their habitat for no reason.
Also, his immediate go to action is violence? Not surprised the co-workers are wary about him. Thats a red flag if ever I heard one.