Actual "swan shot" is not spherical, it is more like an elongated raindrop in shape. A couple of decades ago Headrick gave me a small vial of it but I can't seem to lay my hands on it right now. Here is a video on how to make your own for a muzzle loader.
https://www.bing.com/videos/search?q...tail&FORM=VIRE
This guy's "swan shot" is far less uniform than I remember the stuff Headrick gave me..
From this 1905 ad it appears the Winchester Model 1897 and Winchester LEADER or REPEATER shells are just the ticket for the big birds.
Swan ad 1905.jpg