I can see that this is an old thread but looks like there is some activity here, so I'll write what I know.
In my experience, skills like the press to handstand are better worked by breaking them down and doing each component on its own. And by bringing them all together afterward, you get a press to handstand.
For the purpose of this write-up, I will assume you are talking about a pike press to handstand.
So if we look at this skill, I would break it down as follows:
- Shoulder stability
- Compression strength
- Hamstring flexibility
- Shoulder flexion flexibility
- Wrist extension flexibility
1. Shoulder stability (& straight arm strength)
This area is crucial. If you don't have shoulder stability, your shoulders will not be able to support your weight when you lean on them. Furthermore, you need straight arm strength to make sure you don't turn your straight-arm (SA) press to handstand into a bent-arm (BA) press to handstand, which is a different skill.
Basically, if you can do a SA Press to handstand you can also do a BA Press. It doesn't necessarily go the other way around.
2. Compression strength
Compression strength represents your ability to bring your knees to your face (not your face to your knees!).
If you don't have compression strength (read hip flexors strength) you will find it very hard to take your feet off the ground. Honestly, I feel like it also helps a lot with moving the legs away from your body when pressing up, even though it is the opposite movement.
3. Hamstring flexibility
If you lack this you won't be able to keep your knees straight. You will have to make up for it by either leaning more (which requires more strength!) or bending the knees. Either way, you will have a hard time bringing your hips over your shoulders.
4. Shoulder flexion flexibility
Again, lacking this will force you to lean more on your wrists and, again, require way more strength than necessary, turning your press to handstand into a planche press to handstand (exaggeration, but you get the point).
5. Wrist extension flexibility
If you lack the wrist extension flexibility you will have to make up for it with crazy amounts of hamstring flexibility, shoulder flexion, and compression strength. Again, not ideal.
Ok so what I recommend, now that you know what can happen if you fall short in any of the areas, is to start working on all of them. You don't need to be a master in all. However, if you miss any of them, you will have to compensate a lot in the other areas, to make up for that stubborn one.
Working on the mentioned areas:
1. Shoulder stability: at the end of your workout, do 3-4 x (5-8)
Pike Press Walks (YouTube video linked on the name of the exercise)
2. Compression strength & hamstring flexibility: you can easily pair these; twice a week do a yoga forward folding routine for the hamstring flexibility, at the end of which you would do 3-4 x (8-10) seated pike compression, holding your legs up for 10 seconds in the last repetition of each set, for the compression strength.
You can also incorporate the seated pike compression in the warm-up or at the end of a workout.
The hamstring flexibility can be worked on separately however you want. Personally, I found follow-along yoga forward folding routines to be the most beneficial.
3. Shoulder flexion flexibility: I like the puppy pose from yoga. Get in a puppy pose and do 10-15 pumps followed by a 30-60s hold in the bottom position. Repeat 3-4 times.
(To save time, you can do these as an active rest during your leg day, because they will not interfere with your training)
4. Wrist extension flexibility: during your warm-up, spend 5 extra minutes working on your wrist extension flexibility by leaning on it and doing pumps (10-15) then holding for 30s. Do it for 3-4 sets.
The value of breaking the movement down is that you don't have to do all the exercises at once. Just sprinkle them throughout your day/within your workout routines, so that you have a frequency of 2-3 for each exercise (doing each exercise twice or three times a week).
If you have any other questions let me know.
Good luck!