Maybe in Hawaii in 1893, the answer to the struggle between Lili'uokalani and the annexationist Provisional Government was to keep the monarchy--but get a monarch more acceptable to the
haoles than Lili'uikalani was? Some of the British community in Hawaii liked that idea--especially because of the candidate to replace Lili'uokalani:
"Wodehouse's reference to Princess Ka'iulani was an expression of a plan being considered by English residents in Hawai'i, headed by Theophilus H. Davies, a businessman and longtime resident, to persuade Lili'uokalani to abdicate in favor of her niece. Ka'iulani, then 17 years of age, was the daughter of Lili'uokalani's younger sister Miriam Likelike and Archibald S. Cleghorn, a Scotsman. Raised with British schoolmasters and at that time completing her education in England, Ka'iulani was considered thoroughly British in her outlook. In late 1891, she had been designated heir to the throne by the childless Queen. Davies, who was Ka'iulani's mentor and guardian, considered this a fortunate circumstance, and for some time he had been working to make Ka'iulani as British as possible through education. Her claim to the throne was clear, and if Lili'uokalani agreed to abdicate, Ka'iulani would become queen, and through her the objects both of increase of British influence and an anti-annexation government policy could be achieved. Davies advanced this idea to the British Foreign Office with Wodehouse's approval.13 Many people in Hawai'i, including Dole, would have been satisfied if Ka'iulani had become queen, but it was not a practical idea. The Americans, who had largely engineered the Revolution, were tired of the Monarchy and had previously declared the Monarchy ended. They wanted annexation as a way of ending Hawai'i's constant political squabbling.14 Presumably too, these people would not tolerate for long a sovereign with pro-British sympathies, no matter how circumspect she might be about expressing them. On the other hand, the placing of Ka'iulani upon the throne would probably have stopped the current moves toward annexation and assured an immediate future of greater Hawaiian openness toward the extension of British interests. The British government neither supported nor discouraged this scenario, but if it had come about the government would probably have been satisfied with it..." Ernest Andrade, "Great Britain and the Hawaiian Revolution and Republic, 1893-1898."
https://evols.library.manoa.hawaii.edu/bitstream/10524/562/2/JL24097.pdf
Is it as certain as Andrade writes that it "was not a practical idea"? After all, the anti-annexationist Cleveland had become president, and, as Andrade writes, "believed that the United States, by acting against Lili'uokalani, in effect, had a moral obligation to restore her to her throne. His attempt at restoration ran afoul of the Queen's initial determination to punish those who had rebelled against her and ultimately was undone by the unexpected determination of the leaders of the Provisional Government not to accept the restoration of the Monarchy even with the power of the United States thrown against them." But if it is true that "[m]any people in Hawai'i, including Dole, would have been satisfied if Ka'iulani had become queen" maybe the Provisional Government might have been less determined to resist an American-backed restoration of the monarchy--as long as it was not headed by Lili'uokalani. Dole's approval might reassure Americans worried about Ka'iulani's British connection. Even those Americans anxious for annexation would have to realize that it would not be happening immediately anyway with Cleveland in the White House--so at least in the short run might not a compromise be acceptable (especially if Cleveland hints he will use force if necessary to impose it)? This would leave Lili'uokolani herself as an obstacle, but--yes, I know this is unlikely--maybe she could be convinced that her abdication was the only way of saving the monarchy and preventing annexation?
One problem is that while the immediate causes of her death in 1899 might be butterflied away ("In 1898, while on a horse ride in the mountains of Hawaii Island, Kaʻiulani was caught in a storm and came down with a fever and pneumonia. Earlier she had caught cold from swimming while on the Big Island, and this worsened matters. Kaʻiulani was brought back to Oahu where her health continued to decline. She died on March 6, 1899 at the age of 23 of inflammatory rheumatism."
https://en.wikipedia.org/wiki/Kaʻiulani) her health would probably still not be good, and she still might die relatively early. ("Numerous documented symptoms may indicate she suffered from thyroid disease which would help explain her early death.")