Yep, its the centre hole.

Just did the same thing last week.  I used a 1/2" drill bit then rounded the hole out a fair bit more, and the new button actually screwed into the hole i made.

The only thing is the button has two small locating lugs to seat it into the hole  - you could dremel a slot out for these, or cut them off so it sits flush, or do what i did and let the button sit up a couple of mm.