This situation does not seem normal. If the cygnet had to swim instead of fly to the parents, there may be a problem with either the flight feathers being abnormal or missing. If the cygnet is under 4 months of age, it probably can't fly. If it is approximately 6-8 months of age, it should be flying.

In any case, you might attempt to get friendly with the cygnet so that it will come to you with bread. Let it get comfortable with you to see if you can entice it on land and capture it. If so, then we would suggest that you transport the cygnet to an avian veterinarian or a waterfowl rescue facility for an exam to see if it can fly or if there is an anatomical problem. If the cygnet cannot fly, it needs to go to a rescue facility so that predators cannot catch and kill it. It also needs to be protected from the severe winter and will probably not survive if it cannot migrate to warmer temperatures as presumably the parents have departed. The Regal Swan