Yeah, there will be absolutely nothing on Sin, Cos and Tan trigonometry, so you don't need to worry about the triangles involving SOHCAHTOA, nor do you need to worry about the Sine and Cosine rules if you're doing higher.
However, there may be a question on f(x) graphs, as they just require theoretical movement- f(x-2) doesn't require a calculator, just the knowledge that you add 2 to the x.
As the previous poster said, anything that involves unusual calculations, such as 4/3 pi r^3.
Also, it is highly unlikely that arcs and sectors will come up BUT I am sure for a fact that it will come up in the calculator paper.
Typically, non-calculator questions won't be particularly difficult; the main skill they're testing, really, is how well you can calculate and do maths when you haven't got a calculator.