So it's very hard to answer this counter factual because it really depends on how far back we are rewinding time and trying to guess what happens next. For the purposes of a (hopefully) coherent response, I am just assuming that we rewind to the mid-1880s when the Kingdom of Hawaii was essentially whole.
At its most basic level, I would say no, it is not all that likely another power would have.
By 1898 the age of imperial expansion, or the race for the Pacific, was over. Arguably 1898 was really a last gasp for imperial expansion in the Pacific as the US leveraged the Spanish-American War to purchase control over Guam and the Philippines from Spain which was then followed in 1899 by an agreement between the US and Germany to divide Samoa. The one territory whose status remained uncertain was Vanuatu (then the New Hebrides) which had had both a British and French presence since 1887, though in 1906 the two agreed to a joint administration over the islands. While islands did change hands after this point, any territorial shifts occurred in the context of the First World War and division of Germany's former colonies across Micronesia, Samoa, and New Guinea.
In addition to the end of imperial expansion, it is very important to acknowledge Hawaiian diplomacy. Hawaii had international treaties with Britain, France, and the United States and had been proactive in international affairs. King Kalākaua had undertaken a world tour in 1881 during which he paid official state visits to various rulers, from the Emperor Meiji to Queen Victoria. Diplomacy and demonstrations of legitimacy-- the new symbols of a nation state from flags, to anthems, to royal orders, to new technologies such as electric lighting in ʻIolani Palace in 1887-- were all intended to impress upon others the natural right of Hawaii to participate in international affairs. These public displays differentiated the Kingdom from other indigenous polities that Europeans had dismissed or ignored during their colonial expansion in the nineteenth century. Indeed, Hawaii even had a presence at the Exposition Universelle in 1867 and 1889 in France as part of its diplomatic and cultural outreach.
Sovereignty was a pressing concern for the Kingdom as it had been threatened earlier in the nineteenth century. The French invaded twice, in 1839 and 1849, under the pretext of protecting the religious freedom of Catholics and the rights of French merchants (a similar justification was used for the invasion of the Kingdom of Tahiti). The British had invaded in 1843, though ultimately the leader of that British adventure, Lord George Paulet, was reprimanded by the British Rear Admiral Richard Thomas and forced to withdraw. In the wake of these entanglements, France and Britain agreed to recognize Hawaiian sovereignty (so did the US). This was a good deal for all parties involved as Hawaii guaranteed its independence and the British and French could direct their resources toward armed resistance/war in Aotearoa (New Zealand) and Tahiti.
So why would no other power seize Hawaii if the United States had not? Simply put, the age of empire had essentially ended in the Pacific and there was broad agreement that Hawaiian sovereignty was recognized.
However, even if we imagine US not occupying Hawaii, its presence on the islands is important to consider as US was not prepared to see any one else seize the islands. The US had commercial, cultural, and military entanglements on the islands, for instance in 1875 the US signed a Reciprocity Treaty with the Kingdom granting them a lease to establish a naval station at Pearl Harbor. Assuming Hawaii remained independent, it stands to reason that the US lease on Pearl Harbor and the development of a naval station would have continued in one form or another. We could speculate all day how developed the naval station might have become, but considering the importance of Hawaii as a way station in the Northern Pacific, it is not hard to imagine that the US presence would have continued in order to support ships crossing to the Philippines or US interests in East Asia. Additionally, Hawaii became closely tied to the US during the 19th century-- during the 1840s and 50s especially, its missionary schools were the place many elites on the West Coast sent their children (see for instance Governor Romualdo Pacheco of California). Americans also owned large plantations and shipping businesses in the Kingdom and I do not think it a huge stretch that the US would have intervene to prevent its citizens and interests from being impinged upon by another empire-- especially, considering the "yellow peril" of the early 20th century, the ascendent colonial empire of Japan.
I said at the beginning this gets really complicated based on how far back we want to rewind because the occupation of Hawaii by the US only occurred in 1898 and only occurred because of events beginning most immediately in 1887. That year a group of wealthy planters and businessmen as well as their armed militia, the Honolulu Rifles, forced the King to accept a new constitution, known as the Bayonet Constitution, which stripped the monarchy of much of its power and instead empowered a new cabinet made up of members of this wealthy cabal. This group then overthrew the monarchy entirely in 1893 after Queen Liliʻuokalani attempted to promulgate a new constitution. This wealthy group formed the Committee of Safety and announced martial law, marines from the USS Boston intervened on behalf of this group to prevent royalists from rallying to queen. Thereafter this coalition of planters and business leaders formed the Republic of Hawaii which directed much of its attention to achieve annexation by the US. I am grossly oversimplifying, but the important takeaway is that the late 1880s and 90s were a complex time and depending on where we pause and split the timeline, the question of would Hawaii have been annexed by another power might be different.
I do not have a clear answer at the moment as to what would have happened had the US explicitly disavowed annexation in 1887 or 1893 or 1898. I do not know that I can even begin to make an informed speculation as to whether or not the Kingdom could have been restored or if the Republic would have sought membership in the Commonwealth and the greater British Pacific or if France and England could have been persuaded to intervene in the overthrow.
Some useful sources to learn more because I certainly do not do the topic the full justice it deserves. I tried to include a few that are easily accessible:
Stacy L. Kamehiro, "Hawai‘i at the World Fairs, 1867–1893," World History Connected Accessible Here
Kealani Cook, "Kalākaua's Polynesian Confederacy:Teaching World History in Hawai‘i and Hawai‘i in World History," World History Connected Accessible Here
Noenoe K. Silva, Aloha Betrayed: Native Hawaiian Resistance to American Colonialism
Noelani Arista, The Kingdom and the Republic Sovereign; Hawai'i and the Early United States
Jon Kamakawiwoʻole Osorio, Dismembering Lāhui; A History of the Hawaiian Nation to 1887
Lilikalā Kameʻeleihiwa, Native land and foreign desires
Lorenz Gonschor, A Power in the World: The Hawaiian Kingdom in Oceania
Carol A. MacLennan, Sovereign Sugar : Industry and Environment in Hawaii