Yes, go ahead and capture the cygnet as the parents know there is something wrong and they are not going to risk a predator capturing it and the rest of the family, so they will sacrifice the hurt cygnet.

Take the cygnet to a wildlife rehabilitation center or a zoo. The swan will do well without the web as we had the same thing happen to one of the swans at a facility that we act as consultants. The veterinarian may need to trim the web and suture if necessary and/or provide an antibiotic. In any case, do not allow anyone to euhanize the bird because of the loss of webbing. The bird may have a bit of difficulty getting in and out of water, but as it ages, it will do just fine.

At this young age, captivity and raised by people will be the optimal solution. Please let us know how this situation progresses. The Regal Swan