Hawaiʻian kai: "sea" and Japanese 海/かい/kai: "ocean, sea", definitely no relation. They come from *tasik and something like *m̥ˤəʔ, respectively
On the other hand, Hawaiʻian ʻīlio: "dog" and Japanese 犬/いぬ/inu: "dog" are plausibly (but not certainly) related, from something like *(ŋ)kuɣ(kuɣ)
