Handstands are so fun. I used to do it every day. But if you want to be able to hold without the wall, then you should learn how to progress from there. You can try without the methods if you are brave enough but I personally recommend not doing so for safety reasons.
I don’t teach handstands during personal sessions normally. So far there are two clients who I taught, though lol.
Prerequisite for Handstand
You need to have certain shoulder strength for sure as well as shoulder flexibility. If you are kyphotic, I am not sure doing handstands is a good idea. Get better posture for your shoulders.
Handstand on wall
First you need to get rid of the “fear” that you get from being upside down. First attempt would be scary but you will get used to the movement. Once you will be able to hold the position, move on to the next step.
Handstand feet away from the wall
Try this as the next step. You want to perform a handstand slightly away from the wall. Starting with against the wall, from there, get one leg away from the wall.
The most important thing here is to learn where the hip is. In order to hold the handstand position, the hip should be right above your wrists and shoulders. Then try to take off the other leg away from the wall. It will take quite some time to understand but you will in one day for sure.
Handstand facing wall
This can be scary without knowing how you should fall and rollout. Make sure you learn that first and do this method. What you want to do here is pretty much the same as the last method. Try to get the hip right above your wrists and shoulders, then leave one leg from the wall and the other.
This method and back against the wall are great because you will learn how to control the upside down position for both ways.