Hawaiian independence as a kingdom is difficult;
Is what it says on the tin.
Without major 180s in the space-time continum (i.e. no US westward expansion, which requires a POD of Marianas Trench proportions) then Hawaiian independence as a kingdom is difficult, largely because of the strategic position. Likewise, a random European power planting the flag is unlikely because of distance. The Russians and French tried, but it didn't take; even the British tried (sort of) but gave it up as not worth the effort, as well.
The Hawaiians managed to play the British and Americans off each other for a few decades (as per the flag), but the economic life of the island was largely in the hands of American emigrants by the 1850s or so, and the islands are
much closer to the US West Coast ports than to those of any other power (and the British had much more lucrative places to spend their resources in the Pacific in the Nineteenth Century than the eastern Pacific.) The islands were pretty much acknowledged as part of the US sphere of influence by the 1880s, certainly after the Samoa Crisis.
And if Hawaii is still independent as a monarchy in the 1890s, an internal republican revolution is certainly a possibility, with or without formal US aid.
The other point is that by the end of the century, the obvious importance of Hawaii as a bastion protecting the US West Coast is clear; the "triangle" of Alaska-Hawaii-Panama was appreciated as far back as Schofield's mission in the 1860s.
If Hawaii is independent in the Twentieth Century and has no guarantee of protection by the US (which seems extremely unlikely for obvious reasons), then Hawaii is an obvious target of the Japanese - everything else being equal.
Which will not be a pleasant experience for the Hawaiians, no matter their ancestry.
Best