Your hand position in handstand pushups is not often addressed, even by those that teach the benefits of this exercise. Yet this small piece of positioning makes a BIG impact.
In short, by having your hands out a bit wider, it changes the length of the range of motion, thus making handstand pushups easier.
By having your hands in closer, it increases the range of motion, thus making handstand pushups harder.
You can easily see this difference by putting your arms overhead outside of shoulder width. Now move them to inside of shoulder width, and notice how much higher they are. Break out the tape measure if you need too.
Yes, this will change up the use of the shoulders and triceps to some degree, but the biggest difference will be in the range of motion.
Of course, these are within reason. Too wide and the leverage in the shoulders changes dramatically thus changing the exercise. But within a certain range this tip can be used to adapt the difficulty of this great exercise.