Swans and Geese can be quite viscous in their attacks. I've seen them chase dogs, cats and people away from their protected areas. As an adult I have never been attackted by either one. As a 7 or 8 year old I was. My cousin a year or two older suffered a broken arm in the melee. At that age they may as well be pit bulls. Ma came running out and shooed them away with her broom before they did anymore damage. Their bites and wing beats left a lot of bruising. Remember, in the wild they successfully chase off Arctic Fox and most other predators.
When you are in the water, the only thing sticking out is your head. Of course they will try to beat it down. What else is there to attack? Generally they will only attack if they feel threatened. If they attack you when you're in the water it will appear they are trying to drown you. They are trying to drive you off. Once that is accomplished they will just posture and keep you at bay.When we were attacked by the geese, we went to close to look at the new goslings. When we went out later and kept our distance, they hissed and raised their wings but, didn't attack.
As a 200 lb adult I was attact by some geese I was trying to herd into an enclosure. The nips were somewhat more than I expected. Their wing hits were a bit more painful than I had thought they would be. Once I pinned their wings down and covered their eyes with my other hand when I grabbed their beaks they calmed down. As I carried the goose to the pen the others followe hissing and flapping their wings. When I released the goose I was carrying, they calmed down a bit. They still did their posturing for quite a while.
I suppose if I had run around screaming like a little girl they would have attact en masse. An entire gaggle could have inflicted a bit of damage. Mostly people who get hurt badly by them panic and stir up the geese into a frenzy. A pack of wolves can easily bring down a full grown moose.
The only time I engaged swans was when three of them escaped from a pond they were being shown in. An eatery had them for show. They flew out and landed in traffic. I stopped the car and hered them to the side of the road. I told my wife I'd drive them to the eatery go there and wait.
I put my hand behind its head and walked it to the enclosure. The other two followed closely raising a fuss. As soon as they were safely in their pond they relaxed. Swans can be a handful but they take a backseat to a serial "KIller Whale>"