What type of degree should I look to for new weapons design and manufacturing?
What kind of weapons?
Knives = metallurgy
Guns and ammo = Mechanical engineering, machining/metallurgy or Chemical engineering.
Ships, planes and tanks = Mechanical/Aerospace engineering, Naval architecture.
Electronic warfare = Electrical engineering
Cyberwarfare = Computer science and Math.
Nuclear weapons = Nuclear engineering and Physics
Chemical and Biological weapons = Chemical engineering and Microbiology.
Psychological warfare = Psychology and Marketing
Financial warfare = Economics and Finance
... basically any career can teach you how to create weapons, but only a good conscience can motivate to create solutions.