Sadly it cannot be done this way, at least on my accordion. The "unscrew a bit" is no option because the buttons are glued on, not screwed.
What needs to be done is 1) buy all new buttons, screw-in type, 2) print new "caps" that go over the old stems, have angled top edge and a tiny also angled hole for the screw, and that raise the height of the buttons by 3mm (so the buttons will not hit the plate underneath when pressed) and then 3) glue the tops on, ensuring their top is pointing the right way and finally 4) screw the buttons in (after the glue has dried completely).
It is a rather involved process, but I think it's possible.
Note that 1) caps over the old stems are possible because the holes in the plate are large enough as a whole button can go through them and 2) you don't need the normal felt rings under the buttons because the flat keyboard has felt dampers under the keyboard just like with a piano keyboard.
An even fanciers option would be to also buy a new stepped plate to go under the buttons (to replace the flat plate that's already there). But when you buy such a stepped plate it comes without holes so you have to then drill about 100 holes for the stems to go through...