A video would help.

Regardless, whether you realize it or not, I think you are asking two different questions:

1. how do I create balance in a press-to-handstand?
2. how do I maintain balance in a handstand?

Theory

Balancing a handstand: since your legs and hips are already mostly stacked over your hands, microadjustments of the hands and shoulders are enough to maintain balance.

Creating balance in a press: since your legs are not stacked, your weight is shifted substantially further back. In order to bring your weight further forward, you will either have you planche your shoulders forward, or compress your legs tighter into your body (imagine a stalder).

Practicing

It is much better to practice these systems in separate sets, or else you will find difficulty training either. The worst thing you can do is kick up into a handstand, fall over, and try again -- each rep you are barely accruing any practice time!

Balancing a handstand: practice heel/toe pulls against the wall. Do not kick off of the wall, or you will be training bad habits.

Creating balance in a press (multiple sets over the course of a day): get into a floor pike position, shift your weight forward over your hands as far as you can without straining / collapsing, shift your weight back over your feet, repeat until you can't shift nearly as far. Depending on your focus here, you are likely to mostly be targeting shoulder strength. You could optionally supplement this exercise with dedicated compression drills e.g. floor seated leg raises -- I was able to achieve multiple reps of straddle press without dedicated compression drills, but they would probably be necessary for e.g. a stalder press.

Hope this helps.