Handwraps are not intended to pad your knuckles. Bag and training/sparring gloves are designed to provide padding over your knuckles protecting both you and in the case of training gloves your sparring partner.
Handwraps are used to help prevent injuries to your wrist, thumb and the small bones in the back of your hand connected to your fourth finger and pinky finger. There are as many ways to wrap hands as there are boxing coaches. The method shown in these videos is what I have developed over 60 years of wrapping my own hands as well as those of my boxers. This method is used specifically for twill or semi-elastic wraps. Gauze or velpeau wraps used in competition require much different methods. If you have inadequate gloves or an injury to your knuckles requiring additional padding a layer of dense foam or gel shaped with a void over the injured knuckle can be added at any point in the wrapping process.
Feel free to use this guide as you learn to wrap your hands. As you become proficient you may decide to change the wrap to accommodate your specific needs. OK that’s what we do in boxing; adapt the techniques to our own body’s needs and predilections. Go for it!
There are two videos here one showing me wrapping a boxer’s hand with blue twill wraps and the other video showing me wrapping my own hand using red semi-elastic wraps. I ask that you not copy these videos and post them elsewhere.