You can drill the holes with a hand drill no problem. If you are worried try it out on a test piece of scrap mdf. Dont worry about perfectly perpendicular, unless you are drunk or have some perception problems, you can eyeball it close enough. There is a slight bit of wiggle room anyway when you put the button in, and when you screw it tight it will become flush, even if the hole is off a few degrees from perpendicular.
A forstner bit makes the cleanest holes, but is also expensive. If your relative has one the right size use it, if not you can buy something cheaper. A hole saw or spade bit might chip the edges a bit, but this will be covered up by the lip of the button, so you shouldnt see.
Night is correct. Don't worry about it so much about it, its just a hole. Try it out on some scrap and see.