Handstand pushups are a fantastic exercise. They are perfectly "safe" -- obviously, the blood rushing to your head takes some getting used to, and if you're going to pass out, then get back down again
Once you get them down, there are two progressions. One, try them on parallettes, where the longer range of motion makes them incredibly harder. Second, as you do them with support (I assume against a wall), little by little you'll find you'll need less wall support, and the balance requirements add another strength dimension. I still do them against a wall but can get partial reps and occasionally a full rep without touching the wall.
I personally am a big fan of standing shoulder presses: military press, alternating dumbell shoulder press, various push presses, etc. But there's no rule that you can't cycle handstand pushups in and out with such exercises. All are fantastic.