You can fit American style buttons in the hori shell, however the ID is 1 1/8" which in turn is smaller than the 30mm hole in all hori shells. Clearance wise depends on the shell, in this case not a problem. Granted the button is loose, but if centered and tightened proper it shouldn’t be a problem.
What you really want is what Freedom Gundam said. What you are probably playing with right now is a dynamo SF2CE which is a kit conversion. I ended up restoring said cab, it came with and Ultimate stick, like most cabs at the time, not competition, given those were more expensive for the OPs. The old school concave buttons are vertical plungers unlike the later ones which are much better in design.
Now, we can go further back to leaf controls, but I don’t think they were around much with cabs made in the 90’s.
Long story short and best possible option is to get Industries Lorenzo euro competition stick and euro competition buttons. Happ originally in partnership with IL made excellent hardware but IL and Happ split. Suzo came in the picture to join forces with Happ although the quality faltered. IL however has gone independent. IL is from Spain, Suzo I believe is from Mexico.
The only downside to all of this; The IL Super Joystick is now extinct save for those who have them. My favorite American stick by far, leaf microswitches, round actuator, does 4 way if need be, good diagonals, great return to center. Happ owns the design thus the dilemma. Suzo just doesn’t produce the same quality. Small differences make a huge difference in the end.
Tldr: Go to Paradise Arcade Shop or Focus Attack and get Industries Lorenzo hardware.