It’s the finger, wrist and elbow joints and ligaments (your fingers need to act as toes, your arms are now legs) and not learning how to bail safely (if you flip over and don’t have the reflex to cart wheel out).
There's a reason why handstand pushups (often done against a wall for muscle-building/strength purposes) are considered an advanced shoulder exercise. It's sort of the calisthenics equivalent of the overhead press.
I didn’t say they didn’t. But that won’t be the main source of injury. There are smaller and weaker muscles in the chain if you want to achieve a free standing handstand and not just lean on a wall inverted.
Do free floating handstands for time and see what hurts more.
It’s the finger, wrist and elbow joints and ligaments (your fingers need to act as toes, your arms are now legs) and not learning how to bail safely (if you flip over and don’t have the reflex to cart wheel out).