You can use a router, jigsaw, Dremel, Rotozip... I think a good jigsaw would be your best bet. But Rotozip makes a "guide bit" that, in theory, is perfect for this application. Since there's only a small amount of material to remove, a drum sander in combination with a rasp bit would also work. You could do all of these, with the exception of the jigsaw, with the door right where it is.