I need to cover the top of my head on sunny days to prevent sunburn, and I'm wondering what kind of hat is appropriate to wear in cities in Germany. (I will also be in Austria and Switzerland, but we'll ignore those countries so that this can stay in the Germany forum.)

I'm a middle-aged man who dresses conservatively but casually, so figure that if the day is warm, I'll be wearing a sport shirt, dark trousers, and black shoes with rubber soles. If it's chilly I might also wear a sport jacket or sweater, or a rain jacket if it's rainy.

Any hat needs to be readily packable - I plan to travel with only one bag - and not overly warm.

I don't want to look like I'm dressed for hiking, fishing, hunting, the outback, or a safari, which eliminates many, perhaps most, travel hats. At home I'd probably wear a baseball cap, but that feels all wrong for a German city.

I'm not trying to pass as German, although I speak moderately good German (with an American accent). I just don't want to stand out or look like I don't know where I am.

So the first question is: what kind of hat would a German man of my age, dressed in similar clothes, wear in the daytime? The second is: is there a packable version of such a hat?

I'm not averse to buying a hat in Germany if the recommendation is something more available there than in the U.S.

[Clarification: I'm posting this in the Germany forum because I want information specific to Germany. This is not a general question about travel hats.]