You seem to be doing exactly what needs to be done for the young bird. You were correct in rescuing the cygnet as it probably would not have survived.

Keep him in a warm container with a non-slick surface such as a towel or sheet. Be careful that he cannot suffocate with the bedding. But, he needs a non-slick, non-abrasive surface to protect his legs and feet.

Give him cracked corn and poultry layer pellet submerged in water so he does not choke while eating. Give him fine chopped lettuce on top of the water. Place his food in a small tray or other zero entry container so he can sit or float in the water ( 1-3 inches of water) to eat. Provide him with 2-3 (10) minute supervised baths a day. Watch him closely because he can drown if left for too long. The water needs to be warm and he needs to be dried thoroughly after each bath with a towel. Allow him to preen himself in a warm non-draft setting-good ventilation.

You cannot teach him about predators. He needs to learn this from other birds. If you can place him with young ducks or geese and raise him with other birds when he is about 4 months of age, you will afford him a better chance of survival. He cannot be placed in an unprotected pond due to predators. He needs to be raised with young birds such as other cygnets, geese or ducks with limited contact with older birds so he is not attacked. He should not be introduced to an open habitat until he is at least 6 months of age and can reach a size that hawks, owls, turtles etc. cannot attack him. The Regal Swan