You can perform a handstand push-up against a wall. But eventually, you should work up to performing the push-up from a free balancing handstand, which is by no accounts an easy feat!
Because you’re inverted, this movement naturally falls into the vertical pushing category. It’s more difficult than the standard push-up because you’re moving a higher percentage of your body weight and you’re doing so from a less advantaged position.
Here are the steps to the handstand push-up:
Find a spot in front of the wall, and with your back toward the wall, place your hands on the floor shoulder-width apart fairly close to the wall.
Keeping your elbows locked, kick your feet up so you’re inverted and balanced against the wall.
Organize yourself in this inverted position. Shrug your shoulders up so they cover your ears, keep your belly tight (try to flatten out the arch in your back), put your legs together, and point your toes.

Spend as much as you need to get used to this position before attempting a push-up.
Start to bend your elbows and lower yourself into the handstand push-up, moving your head closer to the ground.

You want to get your head as close to the ground as possible, but don’t bang it. Keep everything super tight and maintain the stiffness throughout your entire body. Don’t force it. If something doesn’t feel right, come out of the handstand.
When your head reaches the floor, press back up into a full lockout to finish the movement.
If you aim to conquer the handstand push-up, you need to be patient.