I would like to keep the original 175/185 70/R13 tires too, and have been told by others to look at Continental Conti Eco 3 tyres. These are only available in T (190kph) speed rating, but I think this might be OK in Denmark as long as one doesn't exceed it. But there could be a problem in Germany, even for me visiting Germany, so it's probably better to find tires with the H rating (210 kph).
The Nankang CX668 gets good reviews, so definitely a tyre I will consider. They seem to be OK in the rain too. Please update the rest of us, when you get some more kilometers on them.