It is true that engineers have the highest pay directly out of college with a BS. Outside of engineering, accounting is probably the second highest. A lot of people who get engineering degrees though are just using it to basically show their abilities, with no intention of pursuing an actual engineering career. Since engineering is very intense in the analytical and quantitative areas, employers know that somebody with an engineering degree has pretty strong raw abilities in this area that could be refined to suit any number of applicationst. Another thing to keep in mind, accountants are pretty well paid, and in the long-term you would probably make more doing that than in an engineering job (engineering starts high, but doesn't have as much long-term growth as business jobs).
That being said, every engineering curriculum is pretty intensive in both math and science. Typically you take Calc 1-3, Differential Equations, Physics I and II (mayber III, depending), and Chemistry. I am currently studying electrical engineering, and I would say that once you make it past the sciences, it's not that intensive on those concepts. You use a lot more math, laplace transforms to solve circuits, boolean algebra to build logic circuits. However, if labs are one of the aspects of science that bother you, engineering has plenty of labs.
Whatever you choose good luck