More than likely, this is a soft tissue injury such as a twist, sprain or strain. As long as it can fly and land, there isn't much you can do. If you try to capture the swan, it is going to fly away and may get separated from the family or disowned. If the parents think you are trying to capture the injured swan, or they think that the injury is so bad that the young swan will lead a predator to the rest of the family, they will disown it and chase it from the family as well as the habitat.

Then, the young swan is going to have more issues. As long as the parents are watching the cygnet, it is eating, flying and pooping, then nature usually heals injuries quickly if they can be healed with time. If it gets to the point that the cygnet cannot move or is readily captured, then it may be too late. However, this is the only way that you will capture it and not disrupt the family unnecessarily. The Regal Swan