Aloha Bobby,
Mahalo for sending your question to the Big Kahuna. Your question is both timely and interesting.
Let’s start with Mele Kalikimaka, the Hawaiian greeting for ‘Merry Christmas’.
Without the letters ‘r’, ‘s’, or ‘t’, the Hawaiian language has difficulty coming up with a near-sounding substitute for ‘Christmas’ but that’s what kalikimaka is. (‘Christian’ is kalikiano.) Mele is much closer in sound to its translated equivalent of ‘merry’.
Hawaiian for ‘Happy New Year’ reverts to its meaning for translation rather than sound for approximation. Hau’oli Makahiki Hou literally translates as ‘Happy Year New’.
Makahiki is also the name for an ancient, four-month-long festival when all war had to stop. (Not a bad idea in any language.) Makahiki began near the middle of October, so timing with the Western Christmas fits, too.
Have a great, if short, visit to the islands and come back again when you can stay longer. In the meantime, you may wish to visit the Top 20 Hawaiian Words to Learn for your Trip.
Aloha,
Big Kahuna