Hi Jody
This is hardly the forum to discuss swan hunting since we are about swan conservation.
But, since you opened the question, we will answer. Regardless of the caliber used for hunting a swan, it is illegal.
Under the Migratory Bird Treaty Act (MBTA), the only swan that can be hunted is the Tundra Swan by Indigenous people of Alaska. Yes, there are people who may be allowed in various states to hunt swans, but that is because federal and state wildlife officials have lied to the American taxpayer and are violating the Treaty by saying the MBTA was reformed in 2004. Fact, the treaty was never ratified which means federal, state and any individual killing swans, especially Mute Swans are in violation of an international Treaty and can be held civilly liable by taxpayers. This point was brought up in NY in 2017 and the NY DEC and their agents were placed on notice about killing Mute Swans. You will be hearing more about this issue on a national basis in the near future. So, our best advice would be not to hunt any swan. The Regal Swan