If they are in season, then killing them for food is perfectly fine. Many species of water fowl have gotten to problematic numbers in parts of both countries and nobody seems to know what to do about it.
FWIW, swans are natural enemies of most ducks and geese. The pond at work has a pair of swans that are actually rented. I know it sounds crazy, but there are
people that will lease you their swans for goose control. I doubt that you would want to lease a swan, but maybe a fake one might do the trick?