You can get a proper forked tool to lever the centre button out but the do tend to stick in with dirt, and they do get brittle with age as well so best to get some spares if you are going to mess with them, some are longer than others ( if they go through two thicknesses of plastic ) and you need to check diameter of main part as well.. I think 10mm diameter and 10 or 12mm and 16mm long rings a bell when I got some.. the shorter ones are used most but a few go through two thicknesses of plastic.
I generally try to get a screwdriver with a blade of at least 5 or 6 mm wide under the plastic lip and twist handle to lift the centre button. Get side of blade alongside centre button as close to shaft as possible and twist, getting as much contact between side of blade and plastic, but you may need to wiggle one side and then attack the opposite side, but as I said don't be surprised if button breaks as after 10 years they get brittle..