How close together do you need the switches to be? That's what really determines the max switch dimensions. You could certainly put small 8x8mm or whatever keycaps like that on a cherry MX, for example, as long as the caps are >14mm center-to-center.
At a guess from the picture, that keypad probably uses a sheet of rubber domes on top of a PCB for the switch. The underside of the dome would have a conductive pad, which comes into contact with pads on the PCB below it when the button is pressed. If you can find a keypad with the right layout of buttons, you may be able to print replacement keycaps and reuse the sheet/domes/PCB.
Other than that, there are tons of switches out there, all sorts of shapes and sizes and styles, so it's hard to give a recommendation without more info. Do you care about tactile feel? Sealing? Do you need an off-the-shelf keycap (not available for many switches, so this would limit your options)?