Despite the fail, see what I tried;

The coil from Carl arrived and the first test look nice;  a 4x2 round magnet glued on a 0.2mm thich silicon sheet moved very well when switching the coil;

So I decied a small pumped based in a set of tesla coils:

the

The test pump I drilled in an acrylic plate on my 3018 cnc
Then mounting it together with M4 screws resulted in a nice pump pack;
But the magnet did not really move at al. I could here a sound but I think the force was much to small to create a real pump ....