Before handstand 1, I always did exercises very similar to wrist pushups and fingertip pushups, except without the pushup phase: I'd keep my arms straight and just do the wrist portion. E.g. similar to the wrist-walk and fingertip-walk, except both hands go up and down at the same time. I feel like this is a much stricter exercise since you can not use momentum from the pushups to assist the wrists in the ascent phase.
Is there a reason to prefer the pushup variation over the no-pushup variation?