One end goes up to make the other end go down........and in this case you can't get one end to go up by snapping the other end down....unless you want to get really deep into gymnastics voodooisms.
A "snapdown" of the lower body will never lift the upper body into the air, so the best thing is to teach a bhs that allows a good push off at the mid-point od the handstand phase. That's going to take longer, and require more time spent on conditioning and technique, but it will get the right results way before a "snapdown approach" to finishing a bhs.
A good place to start is to watch a good bhs in slow motion or frame by frame, and figure out what gives a bhs the energy/power to make the "pop up" happen. Have the kids work them on a trampoline......it will amplify mistakes and correct attempts, and will help them pop up to a stand.
The shape changes are important as well, but IMO it's counter productive to teach them during a bhs until the kids are gettimg some push off through the handstand phase. Find some other activity like throwing an exercise ball, with straight arms, from a slight backward bow shape finishing in a slight "dish" shape. They'll be able to get in a lot of repetitions and move from shape to shape with resistance provided by the ball's inertia.
