Bearing in mind the groove runs along the whole part I suspect it would probably be better to make it longer at both ends then finish off to length onece the groove is cut. I thought about a 28 mm router cutter but the only one's I've found are bloomin dear ......... certainly not worth it for this one off button. Wondered about mounting it horizontally on the mill, then it's a case of grinding up a cutter ........... if I milled out some of the excess first perhaps an old wood bit (spade type) might grind up OK to finish off.
It's not too important, just trying to add a bit of bling to something ............ so no rush either, ................

CC