The biggest error in HSPUs is a CLOSED SHOULDER ANGLE at the top of the handstand. This means that either the butt, the thoracic, the head, or a combination of the three is leaning into the wall and the hips and shoulders are NOT stacked over the hands.
If you're practicing handstand pushups where you continually LAND in a closed shoulder position, most likely you're also unable to find stability at the top (do you find yourself only pushing up for a split second before crashing back down to the floor?) and you're dealing with or have dealt with some shoulder pain.
Instead, you need to retrain your handstand position. In your handstand, your arms should hide your ears or be behind them. This creates an OPEN SHOULDER ANGLE. Your hips need to be over your shoulders by tucking your tail. This activates those tiny little stomach muscles that connect your torso to your legs, making your body act as ONE UNIT, rather than segmented parts.
Retraining a correct handstand position will not only keep your shoulders, wrists, and lower back safe, but it's also WAY more efficient in the long run.