This was almost certainly taken aboard the steamship Manuka when Houdini was returning from Australia. The ship ported in Suva, Fiji on May 17, so it likely ported in Honolulu around May 25. [See UPDATE.] The local paper noted Houdini's presence, and even reported there were hopes he might perform in the city.
|Honolulu Advertiser, May 26, 1910
Houdini's return from Australia via the Pacific was the final link in a journey that took him around the world. This made him eligible to join the Circumnavigators Club, which he did in 1912.
So, yes, the Houdinis went Hawaiian! If only for a day. Pretty wild.
UPDATE: I've nailed down the exact dates of Houdini's Hawaiian adventure. The Manuka arrived in Honolulu on May 24 at 7:45pm at the Alakea Wharf. It departed the following day, May 25 at 3pm. So the photo above was likely taken on May 25, 1910. Aloha.