Ke and ka are known as Kaʻi.
In Hawaiʻian a noun can not exist on it's own, and a Kaʻi such as Ke or Ka is needed to proceed the noun, literally saying 'here comes a noun'.
Some of the rare exceptions to the 'Ke ao' rule:
ke pākaukau (Table, Desk, Counter)
ke pailaka (Pilot)
ke ʻeke (Bag)
ke pā (Plate)
ke ʻoki (Cut)
ke ʻō (Fork)
ke poʻo (Head)
ke pola (Bowl) BUT Ka pola (the flap of a malo (loincloth))
ke mele (Song)
ke hoa (Friend)
ke CD (Compact Disk, pronounced sēdē )
ke pihi (Button, key on keyboard)
ke pihipoho (Locket)
ke pihi laka (Caps key)
ke pihi hoʻoholo (Control key)
ke pihi kāhoʻi (Return key)
ke pihi kake (Shift key)
ke pihi hoʻokōā (Space bar)
ke pani (Lid, cap, (as of toothpaste tube etc))
ke pani paipu laweʻino (Manhole/sewer cover)
ke poho (Chalk)
ke paʻi (Shot, as in photography, print from a computer)
ke paʻi kokoke loa (Very close-up shot, (as in photography))
ke paʻi kokoke (Close-up shot, (as in photography))
ke paʻi lōpō (medium range shot, (as in photography))
ke paʻi laulā (wide range shot, (as in photography))
Nice list! You can see that the ke goes before pihi and pa'i, so any words that come after that won't affect it. I have also seen ka pā (= yard) to differentiate from ke pā. I believe ke goes before pā in the term Pā CD, but not before CD iteslf (the pā here resembles a "plate"). I like to retain the ke for these exceptions, but remember that certain language groups won't! I've seen textbooks use ka pākaukau and ka 'eke which bothers me to no end haha