toilet to pushbutton

Usually you can do it no problem.
The push buttons can fit the hole where the flush handle was you just put the button together a different way, I know for a fact that you can with Fluidmaster flush valves, they stick out a bit though.
You could blank the hole where the flush handle was and drill the cistern lid but i wouldn't.

you need to measure the hole where the syphon goes though the cistern, an old syphon will be 1 1/2 inches and the push type or 2 inches thus kits will do both
www.screwfix.com/p/fluidmaster-4550073-1-1-2-and-2-button-cable-dual-flush-bottom-inlet/58353