Hi etype,
I dont know what type of conifer hedge you have, so I'll assume it's a Leylanii or similar, these do not sprout from old wood thats been cut back hard, so if you intend to take a lot off the top, cutting down into old wood then you will then rely on the outer branches to keep it looking green.
If it means that you have to cut into old wood (without any fresh green foliage) then I'd be inclined to have a square cut across the top or you might otherwise end up with a brown chamfered line along the top which can be seen from below. Hope thats of some help. Tbird+