This is just my opinion, but geography seems the best one to drop if you plan on going into engineering. Physics is the best subject for engineering background (unless you go into software etc.) so that's a good start.
What I've seen from my jobs is that most people can become a project manager eventually, but not everyone can become a engineer as its a specialist subject. I know some people of all backgrounds, some who were ex military or scientists with little or no engineering knowledge, where they start off into project engineering, and eventually gain enough experience to go into project management. Also a lot of engineers start off technical, but end up moving into project management as it does overlap in most industries.
So essentially keep the physics and maths for sure, and economics would also be a good one for the breadth of knowledge and CV.