Mute swans are known as Mute Swans. There really is no Royal or Polish name, however, this designation was given to the two color variations by swan keepers.

Royal Mutes have taupe colored cygnets with black legs and feet. The adults have reddish orange bills and black legs and feet.

The Polish Mutes have white colored cygnets with taupe colored legs and feet. Adults have orange bills and taupe colored legs and feet.

So, Polish Mute designation is just a color variation known as leucistic and there is nothing wrong with the cygnet.

This leucistic coloration was created centuries ago when someone in Eastern Europe tried to create a pure white swan with no color (albino). The leucistic form was created and shows up due to centuries of inbreeding by mute swans across the world. Swans may carry this silent gene for years and it never appears. Then, one day a cygnet with the coloration is hatched. This occurrence may or may not ever be produced again by these swan parents. In any case, this should be a perfectly healthy cygnet just like its siblings. The Regal Swan