Yes, you can fit a much smaller butto nas long as you allow access
some other way. * The design of cistern is different though, I think.
So you need to choose in advance.

Yes, access important.

But with the Grohe frame/cistern, there's a 3mm-ish bore pneumatic
hose which connects the button to the flush, and can use a wide
variety of push buttons large and small (the large plates are called
"skate plates").