Not to imply that there is anything inherently wrong with "white tennis shoes" or anything else, but to me comfort is much more important than appearance. You will see many different styles of shoes and other clothing on the cruise, both on the ship and on the shore excursions. I even got to a point where I was so foot-sore that I went on a shore excursion wearing sandals with white socks. It made me happier and didn't bother anyone else.
Ocean cruises are more informal these days than in the past, and river cruises are even more informal. Don't be concerned about anything you wear marking you as an American. If you come off the ship and are following the flag, you are an American and everyone knows it. And 99% of the Germans and Austrians are very happy to see you. They are typically pleased if you say "Guten Morgan" but if you say "Good Morning" they will know what you mean and answer pleasantly.
Above all if you have a question about anything, be it where to go, how much to pay, proper etiquette, etc., ask one of the Program Directors or the Hotel Manager. They will almost certainly have a good answer and will never intentionally lead you astray.