We're not aware of any one map, in fact we have been trying to develop one. So, the best that we can do for you is give you the locations of origin for the various species.

Whooper Swan Eurasia-U.K

Bewick (Subspecies of the North American Tundra Swan). Eurasia, Russia

Mute Europe, U.K., North America (There is some discussion if they are an invasive species in North America, but there is research regarding the finding of fossils related to the Mute Swans centuries ago.

Black Swans- Botany Bay Australia

Black-Necked & Coscoroba South America, predominantly
Chile and Argentina

Trumpeter and Tundra Swans- North America (Canada, Alaska, Northern U.S. with migration throughout the Midwest and North Carolina)

The Regal Swan