Either will work. Remember, you're dealing with a bureaucracy that doesn't give people much latitude to think. They want to see education that says Engineering on it, not math, not physics, Engineering.
Depending on the kind of engineering you seek, you might consider taking the Fundamentals of Engineering (FE) exam. With a passing grade on the exam, you can put "Engineer-In-Training" on your resume or CV. that may convince an HR troll that you have what it takes for them to forward your resume to the actual person doing the hiring, and it may short-cut the process of getting a formal engineering education.
Do note that engineering is more than the sum of applied math and physics. Engineers learn many methods and approximations that are not taught to physics students, particularly in the area of thermodynamics, fluid dynamics, and circuits. Do not expect to pass the FE without significant prior study.