Shimano screws are likely JIS drive, not Phillips. JIS drivers will probably fit the recesses properly. Having said that I prefer socket drive over Phillips. M4 x 12 should fit OK, if not it would be easy to grind off the slight extra length.
https://en.wikipedia.org/wiki/List_o...rives#Phillips
https://en.wikipedia.org/wiki/List_o...ves#JIS_B_1012