Zip, if you do it yourself.
But since I'm unlikely to move you in that direction, let me mention this...
I believe you're talking about moving the buttons up, not down or over, and thereby exposing the area where the button used to be, so consider first removing a button from a shirt that's not particularly important to you to see what's left after it's removed, meaning any sort of holes that cannot be covered through pressing with a hot iron.
All shirting material, no matter the quality, is as you know relatively thin compared to most other fabrics, so care in removing the buttons is paramount. Often, inside the shirt behind each button, will be a button-sized piece of fabric that thickens the area where the button is attached so it can't easily pull off the shirt. This is good because when you remove the buttons there will be less chance of cutting the shirt. Good luck with this.
(As a complete aside, I am the opposite of most here. Do not care for the bell-shaped roll. I have always liked the look of a collar when using a collar pin, not because of the pin, but because of what it does, hold the points of the collar down tight right up to the tie knot. Because of the like of that look, I have a few times sewn a button down collar to the shirt halfway up the point, allowing only space for the tie to pop through. Different strokes, etc.)