I am very enthusiastic about martial arts and it has become a hobby, a sport, and a -do, a way of life. But although martial arts have become a way of life for me, it is not my whole life. I am a teenager who is currently working diligently in school and putting a lot of effort and struggle into getting decent grades. I acknowledge that martial arts have become a big part of my life, but I also know that I am at an age when I must work hard for college applications. I put a lot of effort in my karate training, but as of now I seek martial arts as a way of keeping my physique and spirits up, not as a profession. Because of that, I am not willing to go to extremes to toughen up my hands. Is there a way to strengthen and make knuckles bigger without traumatizing them? If not, perhaps there a safer way of using Wolf's law?
It appears that you are a stable young man who knows which aspects of his life are important. Learning all you can in school and college in preparation for later life is the first priority. When you are successful at doing something you enjoy as an occupation, your will have time and money to do all the other things you want to do in life as avocations.
As you have observed, breaking is a training tool that provides feedback on proper technique; punch improperly and it hurts. However, breaking is not, and never has been, a requirement of a good fighter or a good martial artist; it is merely a training tool. Breaking has become a form of entertainment and a way to impress the uninformed public. Being an expert in a particular skill does make you a great martial artist. Being an expert at driving does not make you a great golfer; you must also be an expert at chipping and putting, and understanding and playing the game of golf. Without good fighting skills, the best breaker in the world will get beat by a good fighter with no breaking skills. Breaking does not make you a better fighter, a better forms competitor, a better martial artist, or a better person; it is merely a training tool that provides feedback on the use of proper technique.
To market their product and increase sales, some manufactures create a problem for their products to solve. An example is having non-white teeth. Yellowing teeth may be a problem for some but it is not a problem for enough people to make teeth whiteners profitable. Therefore, manufactures of teeth whiteners created a new problem, non-white teeth. According to them, teeth now should not just be a natural whitish color, they must be bright white; an unnatural color that may only be obtained by using their products.
Breaking was a solution in need of a problem. Breaking, and training for breaking, is painful and may be harmful, so why do it? It is not needed for self-defense, and it is not needed to become a great martial artist. So why do something that does little to make you a martial artist when it may cause an injury that will hamper all your training and may cause problems that will plague you in every aspect of your life until you die. Power breaking is done to impress viewers and to attract new students, since people are attracted to the exotic. Trained martial artists see it for what it is—entertainment.
Doing anything to the excess causes undesired side-effects. Body building is good for all people; excessive body building is not good for anyone. Washing your hands is good; compulsive hand washing is not good. Breaking is good, excessive power breaking is bad.
At one point in his life, Mas Oyama toughened his hands until they were breaking tools, but longer useful as hands. In his later years, he expressed regret for this training, since it caused him hand pain and limited hand movement throughout his later years.
There is no secret ointment or method for hand toughening; the only way is by forging. Different arts have different ways of forging, but they all use the same method, repetitious striking of increasingly harder materials. This method works; hands become striking tools. However, a side-effect forging is that the hands become less useful as hands.
You must prioritize your life. Some things are a waste of time and money, while other things are essential. If you live on a hill in the desert southwest, paying for flood insurance for your house is a waste of money since a flood is not likely to happen. However, fire insurance is necessary since bush fires are a constant threat. Most people will never face a self-defense situation during their lives. Therefore, toughening your hands until you can punch trough a brick wall is useless and a waste of time and money. However, martial art training for good physical and mental health and for enjoyment is a good investment, with the useful side-effect that if a self-defense situation does occur, you will be prepared for it.
Stay with basic, useful karate training and it will be useful to you in all aspects of your life.