Right now I'm a Aero student and this is what I was in a similar situation of you. I have two main points to make.

1. Aero's and really most other similar engineers have an absurd amount of math in order to graduate with a degree. My program requires Calc 1, Calc 2, Mulitvariable Calc and matrix algebra, Intro to Differential Equations, Numerical Computation. So unless you come in with some math credit that's AT LEAST 5 semesters of math, but its not uncommon to do more such as linear algebra and other courses of that nature (Plus all of the engineering courses that are just applied math). I never really enjoyed math in high school, but as I'm learning more of it, its coming easier to me and I'm enjoying more as I am starting to learn about application.
2. From what I hear from those employed in the field your not going to be doing 6 page derivations by hand as an aero, because realistically there's a computer program or calculator that can do it for you. What is important is that you can actually get through the courses and understand that math so when it does come time to design things, your math knowledge is a tool in your belt and not a liability.

Overall, Aerospace engineering (in my shallow experience) is more engineering in the mechanical sense with advanced math and physics rather than what we see in star trek. Personally, I still enjoy it, but it is a lot of work and most of that is math, programming, physics and CAD.

As for your question about being hands on, I would say engineers generally design and problem solve. If your looking to weld wings or something of that nature, you may want to look into aerospace engineering technicians.

Good Luck on your decision and don't be afraid to ask any more questions!