I would never go to the USA without having done the written here first.
IO, the OP is from Germany. He'd have to travel to the UK to get the (UK CAA) written exams out of the way. Doesn't make sense. Might as well do them over there.
Studying the theory beforehand (from an appropriate UK-oriented book series, ie. Jeremy Pratt or Trevor Thom) is a must, of course.