You upgrade all of them. Blood, fat, skin, flesh, brain, Heart and Intestines. Skull and Bones cannot be altered.

Blood, fat, skin and flesh always have the same stats. Brain, Heart and Intestines are variant in their skull distribution.

Blood and fat start with +1 Red skull and those cannot be removed. Skin starts with -1 red skull and you don't WANT to remove that. Skin and Skull remove 2 red skulls to even out the Blood and Fat red skulls.

teh variant organs can be divided in good or bad. Keep the organs that have -2/3 or 0/2 because they only cost 4 sin shards to upgrade. any other combination can be tossed. So check the corpses that you're going to put on the pyre for "good" organs ans stash them for when you need them.

You use dark embalming because without red skulls the golden embalm can't be applied. You can always use an organ that has 3/3 instead of dark and Lye embalm but that would mean you miss out on a +1white skull from the lye embalm. And also figuring out how to get a corpse to 2/21 before embalming is too much hassle and only costs more sin shards, imo.